Numérico.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Numérico.ipynb",
      "provenance": [],
      "authorship_tag": "ABX9TyOrGsXZLOqj8I+wZoNf4aG2",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/AnaGutson/Analisis-Numerico/blob/main/Num%C3%A9rico.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# **Trabajo Practico N°1 - Análisis Numérico**"
      ],
      "metadata": {
        "id": "1rF0IHN3UNoe"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **$\\textrm{Integrantes}$**\n"
      ],
      "metadata": {
        "id": "XQnmABrOH1m9"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "- $\\textrm{Pinto, Nicolas} - 105064$ \n",
        "- $\\textrm{Craviotto, Mateo} - 106255$ \n",
        "- $\\textrm{Gutson, Ana Gabriela} - 105853$ \n",
        "- $\\textrm{Balmaceda, Fernando} - 105525$"
      ],
      "metadata": {
        "id": "nGKLov9HUbH_"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **$\\textrm{Bibliotecas a utilizar}$**\n"
      ],
      "metadata": {
        "id": "JtQVyJaUw-3s"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "import scipy as sp\n",
        "from matplotlib import pyplot as plt\n",
        "from sympy import *\n",
        "init_printing(use_unicode=True)"
      ],
      "metadata": {
        "id": "QqSj_7B-w6zF"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "##**2.** $\\textrm{Interpolacion por Spline}$\n"
      ],
      "metadata": {
        "id": "TzIntQqiq_NZ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "$\\textrm{La tabla 1 contiene las muestras obtenidas de las 3 curvas mostrada en la figura 2.1.}$\n",
        "$\\textrm{Se desea interpolar dichas muestras utilizando 3 splines con frontera ligada.}$\n",
        "$\\textrm{Se deben desarrollar los siguientes puntos:}$"
      ],
      "metadata": {
        "id": "50zuOg65owaf"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![image.png](data:image/png;base64,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)"
      ],
      "metadata": {
        "id": "AnMIZdnVowaf"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        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)"
      ],
      "metadata": {
        "id": "UtwsyX0Nowam"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "###$\\quad$ **a)** $\\textrm{Plantear el problema de interpolacion con Spline con frontera ligada.}$ $\\textrm{Asuma que los coeficientes de los terminos independientes, lineales}$ $\\textrm{cuadraticos y cubicos son de la forma } a_i, b_i, c_i, d_i, \\textrm{respectivamente.}$"
      ],
      "metadata": {
        "id": "rj2J6IRWrmog"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "La forma más común de aproximar polinomialmente por tramos es la **interpolación de Spline Cúbico**."
      ],
      "metadata": {
        "id": "YfTziJwtmHxh"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Condiciones**\n",
        "\n",
        "Dada la función _$f$_ definida en $\\begin{bmatrix}a, & b\\end{bmatrix}$ y el conjunto de nodos $a = x_0 < x_1< \\dots < x_n = b$, las condiciones que se deben cumplir para construir un spline cubico $S$ para _$f$_ son: \n",
        "  \n",
        "\\begin{aligned}\n",
        "&i. &&  S_j(x) \\textrm{ es un polinomio cubico en el subintervalo} \\begin{bmatrix}x_j,&x_{j+1} \\end{bmatrix} &\\textrm{ para cada } j = 0, 1, \\dots, n-1;\\\\\n",
        "&ii. && S_j(x_j) = f(x_j) \\quad  y \\quad S_j(x_{j+1}) = f(x_{j+1}) &\\textrm{ para cada } j = 0, 1, \\dots, n-1;\\\\\n",
        "&iii. && S_{j+1}(x_{j+1}) = S_j(x_{j+1}) &\\textrm{ para cada } j = 0, 1, \\dots, n-2;\\\\\n",
        "&iv. && S'_{j+1}(x_{j+1}) = S_j'(x_{j+1}) &\\textrm{ para cada } j = 0, 1, \\dots, n-2;\\\\\n",
        "&v.  && S''_{j+1}(x_{j+1}) = S''_j(x_{j+1}) &\\textrm{ para cada } j = 0, 1, \\dots, n-2;\\\\\n",
        "&vi.  && S'(x_0) = f'(x_0) \\quad  y \\quad S'(x_n) = f'(x_n).\\\\\n",
        "\\end{aligned}\n",
        "\n",
        "El conjunto de condiciones garantizan no solo que el interpolante es continuamente diferenciable en el intervalo, sino también que tiene una segunda derivada continua. Aún así, no supone que las derivadas del interpolante concuerdan con las de la función en su aproximación, incluso en los nodos. \n",
        "\n",
        "La última condición se debe a que se construirá un Spline Cúbico cuya frontera es ligada. Al trabajar con una frontera de este tipo, se obtendrá una aproximación más precisa que al trabajar con frontera natural.\n",
        "\n",
        "Construir un spline de frontera ligada solo es posible si se cuenta con el valor de la derivada en los extremos de _$f$_. De no poseer esta información, se tendría que construir un Spline de frontera natural. En ese caso, la condición $vi.$ sería: \n",
        "$$vi. \\quad  S''(x_0) = S''(x_n) = 0.$$\n",
        "\n"
      ],
      "metadata": {
        "id": "MYhhvYIdrsyS"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Condición $i.$**\n",
        "\n",
        "Para construir el spline cúbico $S$ que se interpola para la función $f$, las condiciones anteriormente mencionadas se aplican a los polinomios cúbicos\n",
        "$$S_j(x) = a_j + b_j (x-x_j) + c_j (x-x_j)^2 + d_j (x-x_j)^3$$ \n",
        "\n",
        "cada uno en el subintervalo $\\begin{bmatrix}x_j, & x_{j+1}\\end{bmatrix}$ para cada $j = 0, 1, \\dots, n-1$, siendo $n =$ cantidad de nodos$ - 1$.\n",
        "\n",
        "Como se puede apreciar, para cada $S_j(x)$ será necesario determinar 4 constantes. Es decir, para construir un spline definido en un intervalo que se ha subdividido en $n$ subintervalos se tendrán que determinar $4n$ constantes."
      ],
      "metadata": {
        "id": "DxllEQmhsDDn"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        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      ],
      "metadata": {
        "id": "ufvhzCLBnHh3"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### $\\quad$**b)** $\\textrm{Mostrar las ecuaciones que permiten obtener los coeficientes de las 3 splines.}$  \n",
        "\n",
        "### $\\textrm{En particular, obtenga el sistema lineal de la forma }$ $A·x = b,$ $\\textrm{ donde}$ $x$ $\\textrm{es el vector de coeficientes correspondientes a los terminos cuadraticos de dichas splines.}$\n",
        "\n",
        "### $\\textrm{Es decir, }$ $x = \\begin{bmatrix} c_0 & c_1 & c_2 & \\dots \\end{bmatrix}^T.$ "
      ],
      "metadata": {
        "id": "vdBf22n_rcD8"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Se tienen $n$ curvas de la forma $S_j(x) = a_j + b_j(x-x_j) + c_j(x-x_j)^2 + d_j(x-x_j)^3$ para cada $j = 0, 1, \\dots, n-1$.\n",
        "\n",
        "Se tienen, entonces, $4n$ constantes a determinar. Para eso, se recurren a las condiciones planteadas anteriormente."
      ],
      "metadata": {
        "id": "ZAHDILMovm9d"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### $\\textrm{Condicion $ii.$}$"
      ],
      "metadata": {
        "id": "0MUUvQ22E0xX"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "\n",
        "Para empezar, los splines deben concordar con los datos en los nodos. Se plantean las siguientes dos ecuaciones generales:\n",
        "\n",
        "- $S_j(x_j) = f(x_j)$\n",
        "\n",
        "Se plantea la primera parte:\n",
        "\n",
        "\\begin{aligned}\n",
        "S_j(x_j) &= a_j + b_j(x_j-x_j) + c_j(x_j-x_j)^2 + d_j(x_j-x_j)^3 \\\\\n",
        "&= a_j + b_j(0) + c_j(0)^2 + d_j(0)^3 \\\\\n",
        "&= a_j\n",
        "\\end{aligned}\n",
        "\n",
        "Y a su vez, esto es igual a $f(x_j)$. Por ende,\n",
        "\n",
        "$ \\quad \\Rightarrow \\quad S_j(x_j) = a_j = f(x_j) $ para cada $j = 0, 1, \\dots, n-1.$\n",
        "\n",
        "- $S_j(x_{j+1}) = f(x_{j+1})$\n",
        "\n",
        "Se plantea la primera parte:\n",
        "\n",
        "$$S_j(x_{j+1}) = a_j + b_j(x_{j+1}-x_j) + c_j(x_{j+1}-x_j)^2 + d_j(x_{j+1}-x_j)^3$$\n",
        "\n",
        "Y a su vez, esto es igual a $f(x_{j+1})$. Por ende,\n",
        "\n",
        "$ \\quad \\Rightarrow \\quad S_j(x_{j+1}) = a_j + b_j(x_{j+1}-x_j) + c_j(x_{j+1}-x_j)^2 + d_j(x_{j+1}-x_j)^3 = f(x_{j+1})$ para cada $j = 0, 1, \\dots, n-1.$"
      ],
      "metadata": {
        "id": "4KylfYSKaGjB"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### $\\textrm{Condicion $iii.$}$"
      ],
      "metadata": {
        "id": "Dxi3GzGyE2td"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "\n",
        "Se sabe, además, que las curvas deben coincidir en los bordes:\n",
        "$$S_{j+1}(x_{j+1}) = S_j(x_{j+1})$$\n",
        "\n",
        "Con el planteo anterior se concluyó que $S_{j+1}(x_{j+1}) = a_{j+1}$, y que además $S_j(x_{j+1}) = a_j + b_j(x_{j+1}-x_j) + c_j(x_{j+1}-x_j)^2 + d_j(x_{j+1}-x_j)^3$.\n",
        "\n",
        "Se puede decir entonces que:\n",
        "\n",
        "$ \\quad \\Rightarrow \\quad a_{j+1} = S_{j+1}(x_{j+1}) = S_j(x_{j+1}) = a_j + b_j(x_{j+1}-x_j)+c_j(x_{j+1}-x_j)^2 + d_j(x_{j+1}-x_j)^3$ para cada $j = 0, 1, \\dots, n-2.$\n"
      ],
      "metadata": {
        "id": "J6vtpfA8THbT"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### $\\textrm{Condicion $iv$.}$"
      ],
      "metadata": {
        "id": "SZD-zOvqE4ds"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "\n",
        "Se plantea la igualdad de las derivada de primer orden de las curvas en los bordes:\n",
        "$$S'_{j+1}(x_{j+1}) = S_j'(x_{j+1})$$\n",
        "\n",
        "Se desarrolla:\n",
        "\n",
        "\\begin{aligned}\n",
        "S'_{j+1}(x_{j+1}) &= b_{j+1} + 2c_{j+1}(x_{j+1}-x_{j+1})+3d_{j+1}(x_{j+1}-x_{j+1})^2 \\\\\n",
        "&= b_{j+1} + 2c_{j+1}(0)+3d_{j+1}(0)^2 \\\\\n",
        "&= b_{j+1}\n",
        "\\end{aligned}\n",
        "\n",
        "Entonces, $S'_{j+1}(x_{j+1}) = b_{j+1}$.\n",
        "\n",
        "A su vez:\n",
        "\n",
        "\\begin{aligned}\n",
        "S'_j(x_{j+1}) &= b_j + 2c_j(x_{j+1}-x_j)+3d_j(x_{j+1}-x_j)^2\n",
        "\\end{aligned}\n",
        "\n",
        "Se concluye entonces:\n",
        "\n",
        "$ \\quad \\Rightarrow \\quad b_{j+1} = b_j + 2c_j(x_{j+1}-x_j)+3d_j(x_{j+1}-x_j)^2$ para cada $j = 0, 1, \\dots, n-1.$"
      ],
      "metadata": {
        "id": "hOglGb45kRh-"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### $\\textrm{Condicion $v.$}$"
      ],
      "metadata": {
        "id": "ME3fmZIaE6n8"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "\n",
        "Se plantea la igualdad de la derivada de segundo orden de las curvas en los bordes:\n",
        "$$S''_{j+1}(x_{j+1}) = S_j''(x_{j+1})$$\n",
        "\n",
        "Se desarrolla:\n",
        "\n",
        "\\begin{aligned}\n",
        "S''_{j+1}(x_{j+1}) &= 2c_{j+1} + 6d_{j+1}(x_{j+1}-x_{j+1})\\\\\n",
        "&= 2c_{j+1} + 6d_{j+1}(0)\\\\\n",
        "&= 2c_{j+1}\n",
        "\\end{aligned}\n",
        "\n",
        "Entonces, $S''_{j+1}(x_{j+1}) = 2c_{j+1}$.\n",
        "\n",
        "A su vez:\n",
        "\n",
        "\\begin{aligned}\n",
        "S''_j(x_{j+1}) &= 2c_j + 6d_j(x_{j+1}-x_j)\n",
        "\\end{aligned}\n",
        "\n",
        "Se plantea la igualdad: $2c_{j+1} = 2c_j + 6d_j(x_{j+1}-x_j)$.\n",
        "\n",
        "Se despeja $c_{j+1}$\n",
        "\n",
        "$ \\quad \\Rightarrow \\quad c_{j+1} = c_j + 3d_j(x_{j+1}-x_j)$ para cada $j = 0, 1, \\dots, n-1.$"
      ],
      "metadata": {
        "id": "lYqdgct5q_Qn"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### $\\textrm{Pasaje en limpio de las ecuaciones}$\n",
        "\n",
        "Se pasan en limpio las ecuaciones previamente obtenidas, las cuales permiten la construcción de un Spline Cúbico genérico, ya que aún no han sido aplicadas las condiciones de borde."
      ],
      "metadata": {
        "id": "0BqHgt-vJMS5"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Se pasa en limpio lo obtenido a partir de las **condiciones** $iii.$, $iv.$ y $v.$:\n",
        "\n",
        "> **($1$)** $\\quad a_{j+1} = a_j + b_j(x_{j+1}-x_j)+c_j(x_{j+1}-x_j)^2 + d_j(x_{j+1}-x_j)^3$\n",
        ">\n",
        "> **($2$)** $\\quad b_{j+1} = b_j + 2c_j(x_{j+1}-x_j)+3d_j(x_{j+1}-x_j)^2$\n",
        ">\n",
        "> **($3$)** $\\quad c_{j+1} = c_j + 3d_j(x_{j+1}-x_j)$"
      ],
      "metadata": {
        "id": "8lQTAtS3rOoz"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Se resuelve el sistema buscando que quede todo en funcion de $\\{c_j\\}_{j = 0}^n$."
      ],
      "metadata": {
        "id": "CNL96xLRwHcI"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Se despeja $d_j$ de **($3$)**\n",
        "> $d_j = \\frac{(c_{j+1} - c_j)}{3(x_{j+1}-x_j)}$"
      ],
      "metadata": {
        "id": "soREsgwOxErQ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Se procede a reemplazar $d_j$ en **($1$)** y **($2$)**.\n",
        "\n",
        "- Se reemplaza $d_j$ en **($1$)**\n",
        "\n",
        "\\begin{aligned}\n",
        "a_{j+1} &= a_j + b_j(x_{j+1}-x_j) + c_j(x_{j+1}-x_j)^2 + \\frac{(c_{j+1} - c_j)}{3(x_{j+1}-x_j)}(x_{j+1}-x_j)^3 \\\\\n",
        "&= a_j + b_j(x_{j+1}-x_j) + c_j(x_{j+1}-x_j)^2 + \\frac{(c_{j+1} - c_j)(x_{j+1}-x_j)^2}{3} \\\\\n",
        "&= a_j + b_j(x_{j+1}-x_j) + \\frac{(3c_j + c_{j+1} - c_j)(x_{j+1}-x_j)^2}{3} \\\\\n",
        "&= a_j + b_j(x_{j+1}-x_j) + \\frac{(2c_j + c_{j+1})(x_{j+1}-x_j)^2}{3} \\\\\n",
        "\\end{aligned}\n",
        "\n",
        "Se agrega una nueva ecuación:\n",
        "\n",
        "> **($4$)** $\\quad a_{j+1} = a_j + b_j(x_{j+1}-x_j) + \\frac{(2c_j + c_{j+1})(x_{j+1}-x_j)^2}{3}.$\n",
        "\n",
        "- Ahora se reemplaza $d_j$ en **($2$)**\n",
        "\n",
        "\\begin{aligned}\n",
        "b_{j+1} &= b_j + 2c_j(x_{j+1}-x_j)+3\\frac{(c_{j+1} - c_j)}{3(x_{j+1}-x_j)}(x_{j+1}-x_j)^2 \\\\\n",
        "&= b_j + 2c_j(x_{j+1}-x_j) + (c_{j+1} - c_j)(x_{j+1}-x_j) \\\\\n",
        "&= b_j + (2c_j + c_{j+1} - c_j)(x_{j+1}-x_j) \\\\\n",
        "&= b_j + (c_j + c_{j+1})(x_{j+1}-x_j) \\\\\n",
        "\\end{aligned}\n",
        "\n",
        "A esta ecuación, se le reduce en $1$ el índice:\n",
        "\n",
        "> **($5$)** $\\quad b_{j} = b_{j-1} + (c_{j-1} + c_j)(x_j-x_{j-1}).$"
      ],
      "metadata": {
        "id": "VzyJkeNXx3ce"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Se despeja $b_j$ de **($4$)**\n",
        "\n",
        "> **($6$)** $\\quad b_j = \\frac{a_{j+1}-a_j}{x_{j+1}-x_j} - \\frac{(x_{j+1}-x_j)(2c_j + c_{j+1})}{3}$"
      ],
      "metadata": {
        "id": "mvZIoSyoG7QH"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Y se reduce en $1$ el índice, tal que\n",
        "\n",
        "> **($7$)** $\\quad b_{j-1} = \\frac{a_j-a_{j-1}}{x_j-x_{j-1}} - \\frac{(x_j-x_{j-1})(2c_{j-1} + c_j)}{3}$\n"
      ],
      "metadata": {
        "id": "tDRMobVGHGsn"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Ahora, a partir de lo obtenido en **($6$)** y **($7$)**, se reescribe **($5$)**.\n",
        "\n",
        "\\begin{aligned}\n",
        "b_j &= b_{j-1} + (c_{j-1} + c_j)(x_j-x_{j-1}) \\\\\n",
        "\\frac{a_{j+1}-a_j}{x_{j+1}-x_j} - \\frac{(x_{j+1}-x_j)(2c_j + c_{j+1})}{3} &= \\frac{a_j-a_{j-1}}{x_j-x_{j-1}} - \\frac{(x_j-x_{j-1})(2c_{j-1} + c_j)}{3} + (c_{j-1} + c_j)(x_j-x_{j-1}) \\\\\n",
        "\\frac{a_{j+1}-a_j}{x_{j+1}-x_j} - \\frac{a_j-a_{j-1}}{x_j-x_{j-1}} &= \\frac{(x_j-x_{j-1})(-2c_{j-1} - c_j)}{3} + (c_{j-1} + c_j)(x_j-x_{j-1}) + \\frac{(x_{j+1}-x_j)(2c_j + c_{j+1})}{3}\\\\\n",
        "3\\frac{a_{j+1}-a_j}{x_{j+1}-x_j} - 3\\frac{a_j-a_{j-1}}{x_j-x_{j-1}} &= (x_j-x_{j-1})(-2c_{j-1} - c_j) + 3(c_{j-1} + c_j)(x_j-x_{j-1}) + (x_{j+1}-x_j)(2c_j + c_{j+1})\\\\\n",
        "3\\frac{a_{j+1}-a_j}{x_{j+1}-x_j} - 3\\frac{a_j-a_{j-1}}{x_j-x_{j-1}} &= (x_j-x_{j-1})(c_{j-1} + 2c_j)+ (x_{j+1}-x_j)(2c_j + c_{j+1})\\\\\n",
        "3\\frac{a_{j+1}-a_j}{x_{j+1}-x_j} - 3\\frac{a_j-a_{j-1}}{x_j-x_{j-1}} &= (x_j-x_{j-1})c_{j-1} + (x_j-x_{j-1})2c_j+ (x_{j+1}-x_j)2c_j + (x_{j+1}-x_j)c_{j+1}\\\\\n",
        "\\end{aligned}\n",
        "\n",
        "para $j = 1, 2, \\dots, n - 1$ .\n",
        "\n",
        "Se obtiene entonces una nueva ecuación:\n",
        "\n",
        "> **($8$)** $\\quad (x_j-x_{j-1})c_{j-1} + 2c_j[(x_j-x_{j-1}) + (x_{j+1}-x_j)] + (x_{j+1}-x_j)c_{j+1} = 3\\frac{a_{j+1}-a_j}{x_{j+1}-x_j} - 3\\frac{a_j-a_{j-1}}{x_j-x_{j-1}}$\n",
        "\n",
        "Esta ecuación tiene como incógnitas los $\\{c_j\\}^n_{j = 0}$, dado que tanto $a_j$ como $x_j$ ya fueron encontrados previamente."
      ],
      "metadata": {
        "id": "tQIq4XymJDt6"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### $\\textrm{Condicion $vi.$}$\n",
        "\n",
        "Se imponen, finalmente, las condiciones de frontera.\n"
      ],
      "metadata": {
        "id": "y7m_MCHJbMX4"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "- $S_0'(x_0) = f'(x_0)$\n",
        "\n",
        "Se plantea la primera parte:\n",
        "\n",
        "\\begin{aligned}\n",
        "S'_0(x_0) &= b_0 + 2c_0(x_0-x_0) + 3d_0(x_0-x_0)^2 \\\\\n",
        "&= b_0 + 2c_0(0) + 3d_0(0)^2 \\\\\n",
        "&= b_0\n",
        "\\end{aligned}\n",
        "\n",
        "Y a su vez, esto es igual a $f'(x_0)$. Por ende,\n",
        "\n",
        "$ \\quad \\Rightarrow \\quad S_0'(x_0) = b_0 = f'(x_0).$\n",
        "\n",
        "Se reemplaza lo obtenido en **($6$)** con $j = 0$ y se obtiene:\n",
        "\n",
        "\\begin{aligned}\n",
        "f'(x_0) &= \\frac{a_1-a_0}{x_1-x_0} - \\frac{(x_1-x_0)(2c_0 + c_1)}{3}\\\\\n",
        "3f'(x_0) &= 3\\frac{a_1-a_0}{x_1-x_0} - (x_1-x_0)(2c_0 + c_1)\\\\\n",
        "3f'(x_0) &= 3\\frac{a_1-a_0}{x_1-x_0} - (x_1-x_0)2c_0 - (x_1-x_0)c_1\\\\\n",
        "\\end{aligned}\n",
        "\n",
        "Se obtiene entonces la siguiente ecuación:\n",
        "\n",
        "> **($9$)** $\\quad 2(x_1-x_0)c_0 +(x_1-x_0)c_1 = 3\\frac{a_1-a_0}{x_1-x_0} - 3f'(x_0)$"
      ],
      "metadata": {
        "id": "XcVRcGSufxVM"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "- $S_{n-1}'(x_n) = f'(x_n)$\n",
        "\n",
        "Se plantea la primera parte:\n",
        "\n",
        "$$S_{n-1}'(x_n) = b_{n-1} + 2c_{n-1}(x_n-x_{n-1}) + 3d_{n-1}(x_n-x_{n-1})^2$$\n",
        "\n",
        "Y anteriormente se obtuvo que\n",
        "$$d_j = \\frac{(c_{j+1} - c_j)}{3(x_{j+1}-x_j)}$$\n",
        "\n",
        "Por ende, \n",
        "\n",
        "\\begin{aligned}\n",
        "S_{n-1}'(x_3) &= b_{n-1} + 2c_{n-1}(x_n-x_2) + 3\\frac{c_n - c_{n-1}}{3(x_n-x_{n-1})}(x_n-x_2)^2 \\\\\n",
        "&= b_{n-1} + 2c_{n-1}(x_n-x_{n-1}) + (c_n - c_{n-1})(x_n-x_{n-1}) \\\\\n",
        "&= b_{n-1} + (c_{n-1} + c_n)(x_n-x_{n-1})\n",
        "\\end{aligned}\n",
        "\n",
        "Y a su vez, esto es igual a $f'(x_n)$. Por ende,\n",
        "\n",
        "$ \\quad \\Rightarrow \\quad S_{n-1}'(x_n) = b_{n-1} + (c_{n-1} + c_n)(x_n-x_{n-1}) = f'(x_n).$\n",
        "\n",
        "Se despeja $b_{n-1}$:\n",
        "\n",
        "$$b_{n-1} + (c_{n-1} + c_n)(x_n-x_{n-1}) = f'(x_n)$$\n",
        "$$b_{n-1} = f'(x_n) - (c_{n-1} + c_n)(x_n-x_{n-1})$$\n",
        "\n",
        "Se reemplaza $b_{n-1}$ en **($6$)** con $j = (n-1)$ y se obtiene:\n",
        "\n",
        "\\begin{aligned}\n",
        "f'(x_n) - (c_{n-1} + c_n)(x_n-x_{n-1}) &= \\frac{a_n-a_{n-1}}{x_n-x_{n-1}} - \\frac{(x_n-x_{n-1})(2c_{n-1} + c_n)}{3}\\\\\n",
        "f'(x_n) &= \\frac{a_n-a_{n-1}}{x_n-x_{n-1}} + \\frac{(x_n-x_{n-1})(-2c_{n-1} - c_n)}{3} + (c_{n-1} + c_n)(x_n-x_{n-1})\\\\\n",
        "f'(x_n) &= \\frac{a_n-a_{n-1}}{x_n-x_{n-1}} + \\frac{(x_n-x_{n-1})(-2c_{n-1} - c_n + 3c_{n-1} + 3c_n)}{3}\\\\\n",
        "f'(x_n) &= \\frac{a_n-a_{n-1}}{x_n-x_{n-1}} + \\frac{(x_n-x_{n-1})(c_{n-1} + 2c_n)}{3}\\\\\n",
        "3f'(x_n) &= 3\\frac{a_n-a_{n-1}}{x_n-x_{n-1}} + (x_n-x_{n-1})c_{n-1} + (x_n-x_{n-1})2c_n\\\\\n",
        "\\end{aligned}\n",
        "\n",
        "\n",
        "Se obtiene entonces la siguiente ecuación:\n",
        "\n",
        "> **($10$)** $\\quad (x_n-x_{n-1})c_{n-1} + 2(x_n-x_{n-1})c_n = 3f'(x_n) - 3\\frac{a_n-a_{n-1}}{x_n-x_{n-1}}$"
      ],
      "metadata": {
        "id": "xG2CtDhVhtSA"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### $\\textrm{Sistema Lineal}$"
      ],
      "metadata": {
        "id": "0u_SkiYuzGrM"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Se juntan las ecuaciones **($9$)**, **($8$)** y **($10$)**. Es decir,\n",
        "\n",
        "- $2(x_1-x_0)c_0 +(x_1-x_0)c_1 = 3\\frac{a_1-a_0}{x_1-x_0} - 3f'(x_0).$\n",
        "- $(x_j-x_{j-1})c_{j-1} + 2c_j[(x_j-x_{j-1}) + (x_{j+1}-x_j)] + (x_{j+1}-x_j)c_{j+1} = 3\\frac{a_{j+1}-a_j}{x_{j+1}-x_j} - 3\\frac{a_j-a_{j-1}}{x_j-x_{j-1}} \\quad$ para cada $j = 0, 1, \\dots, n-1.$\n",
        "- $(x_n-x_{n-1})c_{n-1} + 2(x_n-x_{n-1})c_n = 3f'(x_n) - 3\\frac{a_n-a_{n-1}}{x_n-x_{n-1}}.$ \n",
        "\n",
        "Y se plantea el siguiente sistema lineal: \n",
        "\n",
        "$$\n",
        "  \\left\\{ \\begin{array}{lcc}\n",
        "              2(x_1-x_0) c_0 +(x_1-x_0)c_1 = 3\\frac{a_1-a_0}{x_1-x_0} - 3f'(x_0) \\\\\n",
        "              (x_1-x_0) c_0 + 2[(x_1-x_0) + (x_2-x_1)] c_1 + (x_2-x_1) c_2 = 3\\frac{a_2-a_1}{x_2-x_1} - 3\\frac{a_1-a_0}{x_1-x_0} \\\\\n",
        "              (x_2-x_1) c_1 + 2[(x_2-x_1) + (x_3-x_2)] c_2 + (x_3-x_2)c_3 = 3\\frac{a_3-a_2}{x_3-x_2} - 3\\frac{a_2-a_1}{x_2-x_1} \\\\\n",
        "              \\quad\\dots \\\\\n",
        "              (x_{n-1}-x_{n-2}) c_{n-2} + 2[(x_{n-1}-x_{n-2}) + (x_n-x_{n-1})] c_{n-1} + (x_n-x_{n-1})c_n = 3\\frac{a_n-a_{n-1}}{x_n-x_{n-1}} - 3\\frac{a_{n-1}-a_{n-2}}{x_{n-1}-x_{n-2}} \\\\\n",
        "              (x_n-x_{n-1}) c_{n-1} + 2(x_n-x_{n-1}) c_n = 3f'(x_n) - 3\\frac{a_n-a_{n-1}}{x_n-x_{n-1}}\n",
        "          \\end{array}\n",
        "  \\right.\n",
        "$$"
      ],
      "metadata": {
        "id": "exgRlmQCJ_Pb"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Se coloca la información en las matrices A y b, para así resolver el sistema lineal de ecuaciones $Ax = b$.\n",
        "\n",
        "$A$ resulta en la matriz\n",
        "\n",
        "$$\\begin{bmatrix}\n",
        "    2(x_1-x_0) & (x_1-x_0) & 0 & \\dots & \\dots & \\dots & 0\\\\\n",
        "  (x_1-x_0) & 2[(x_1-x_0)+(x_2-x_1)] & (x_2-x_1) &0 & \\dots & \\dots & 0\\\\\n",
        "    0 & (x_2-x_1) &  2[(x_2-x_1)+(x_3-x_2)] & (x_3-x_2) &0 & \\dots & 0\\\\\n",
        "    \\dots&\\dots&\\dots&\\dots&\\dots&\\dots & \\dots\\\\\n",
        "    0 & \\dots& \\dots & 0 & (x_{n-1}-x_{n-2}) & 2[(x_{n-1}-x_{n-2})+(x_n-x_{n-1})] & (x_n - x_{n-1}) \\\\\n",
        "    0 & \\dots & \\dots &\\dots & 0 & (x_n-x_{n-1}) & 2(x_n-x_{n-1})\n",
        "  \\end{bmatrix}\n",
        "$$ \n",
        "\n",
        "  $$b = \\begin{bmatrix}\n",
        "  3\\frac{a_1-a_0}{x_1-x_0} - 3f'(x_0) \\\\\n",
        "  3\\frac{a_2-a_1}{x_2-x_1} - 3\\frac{a_1-a_0}{x_1-x_0} \\\\\n",
        "  3\\frac{a_3-a_2}{x_3-x_2} - 3\\frac{a_2-a_1}{x_2-x_1} \\\\\n",
        "  \\dots \\\\\n",
        "  3\\frac{a_n-a_{n-1}}{x_n-x_{n-1}} - 3\\frac{a_{n-1}-a_{n-2}}{x_{n-1}-x_{n-2}} \\\\\n",
        "  3f'(x_n) - 3\\frac{a_n-a_{n-1}}{x_n-x_{n-1}}\n",
        "  \\end{bmatrix},$$\n",
        "\n",
        "  $$x = \\begin{bmatrix}\n",
        "  c_0 \\\\\n",
        "  c_1 \\\\\n",
        "  c_2 \\\\\n",
        "  \\vdots\\\\\n",
        "  c_{n-1}\\\\\n",
        "  c_n\n",
        "  \\end{bmatrix}.$$\n",
        "\n",
        "   "
      ],
      "metadata": {
        "id": "agxoDllfZUgB"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### $\\quad$**c)** $\\textrm{Desarrollar el seudocodigo del algoritmo de interpolacion con Spline ligada}$ $\\textrm{en base a lo explicado en los dos puntos anteriores}.$"
      ],
      "metadata": {
        "id": "vC_y-ALi2uD9"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sympy import *\n",
        "init_printing(use_unicode=True)\n",
        "import numpy as np"
      ],
      "metadata": {
        "id": "lnnDN-dgvsr9"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### $\\textrm{Implementacion - Forma 1}$\n",
        "\n",
        "A partir de lo concluído previamente, se propone la siguiente implementación para hallar el polinomio interpolante.\n"
      ],
      "metadata": {
        "id": "ljKyQ6CnzHD6"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Se cuenta con la clase **SplineCubico**, la cual se inicializa con $4$ valores:\n",
        "- $nodos:$ la coordenada \"$x$\" de los puntos a interpolar.\n",
        "- $imagen\\_nodos:$ la coordenada \"$y$\" de los puntos a interpolar.\n",
        "- $fpo:$ la derivada primera de $f(x_0)$.\n",
        "- $fpn:$ la derivada primera de $f(x_n)$. \n",
        "\n",
        "Para generar el spline, se llama al método $construir\\_spline\\_cubico()$. Éste devuelve los coeficientes $a$, $b$, $c$ y $d$.\n",
        "\n",
        "En caso de querer visualizar los $S_j$, se invoca el método $obtener\\_Sj$ enviándole como parámetro el _j_ a utilizar.\n",
        "\n",
        "Y finalmente, en caso de querer visualizar todos los $S_j$, se utiliza el método $obtener\\_todos\\_los\\_Sj().$"
      ],
      "metadata": {
        "id": "ripbXn2GPtTd"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "class SplineCubico():\n",
        "  \n",
        "  #Se inicializa un interpolador cuyos atributos son:\n",
        "  # • nodos: la coordenada \"x\" de los puntos a interpolar.\n",
        "  # • imagen_nodos: la coordenada \"y\" de los puntos a interpolar.\n",
        "  # • fpo: la derivada primera de f(x0).\n",
        "  # • fpn: la derivada primera de f(xn).\n",
        "  def __init__(self, nodos, imagen_nodos, fpo, fpn):\n",
        "\n",
        "    self.a = imagen_nodos\n",
        "    self.x = nodos\n",
        "    self.n = len(nodos)\n",
        "\n",
        "    self.fpo = fpo\n",
        "    self.fpn = fpn\n",
        "\n",
        "    self.b = [None] * (self.n-1)\n",
        "    self.c = [None] * (self.n)\n",
        "    self.d = [None] * (self.n-1)\n",
        "\n",
        "    #uso h_j = x_{j+1} - x_j para facilitar la notación\n",
        "    self.h = [None] * (self.n - 1)\n",
        "    for i in range(self.n - 1):\n",
        "      self.h[i] = self.x[i+1] - self.x[i]\n",
        "\n",
        "  def construir_A(self):\n",
        "    \n",
        "    #Matriz de 0s\n",
        "    A = zeros(self.n)\n",
        "\n",
        "    #Primera fila\n",
        "    A[0,0] = 2*self.h[0]\n",
        "    A[0,1] = self.h[0]\n",
        "\n",
        "    #Resto de filas menos la última\n",
        "    for i in range(self.n-2):\n",
        "      A[i+1,i] = self.h[i]\n",
        "      A[i+1,i+1] = 2*(self.h[i]+self.h[i+1])\n",
        "      A[i+1,i+2] = self.h[i+1]\n",
        "\n",
        "    #Ultima fila\n",
        "    A[self.n-1, self.n-2] = self.h[self.n-2]\n",
        "    A[self.n-1, self.n-1] = 2*self.h[self.n-2]\n",
        "\n",
        "    return A\n",
        "\n",
        "\n",
        "  def construir_b(self):\n",
        "    tope = self.n - 1\n",
        "    b = Matrix([3*(self.a[1]-self.a[0])/self.h[0] - 3*self.fpo])\n",
        "    for i in range(tope-1):\n",
        "      b = Matrix.vstack(b, Matrix([3*(self.a[i+2]-self.a[i+1])/self.h[i+1] - 3*(self.a[i+1]-self.a[i])/self.h[i]]))\n",
        "    b = Matrix.vstack(b, Matrix([3*self.fpn - 3*(self.a[tope]-self.a[tope-1])/self.h[tope-1]])) \n",
        "    \n",
        "    return b\n",
        "\n",
        "  def lusinpivot(self, A, b):\n",
        "    A = np.array(A.tolist())\n",
        "    n = A.shape[0]\n",
        "    U = A.copy()\n",
        "    L = np.eye(n, dtype=np.double)\n",
        "\n",
        "    for i in range(n):\n",
        "        factor = U[i+1:, i] / U[i, i]\n",
        "        L[i+1:, i] = factor\n",
        "        U[i+1:] -= factor[:, np.newaxis] * U[i]\n",
        "\n",
        "    return Matrix(L), Matrix(U)\n",
        "\n",
        "\n",
        "  def resolver_sistema_lineal(self):\n",
        "\n",
        "    A = self.construir_A()\n",
        "    b = self.construir_b()\n",
        "    #x = A.gauss_jordan_solve(b)[0] #se obtiene la solucion única de Ax = b\n",
        "    L, U = self.lusinpivot(A.copy(), b)\n",
        "\n",
        "    # Se sabe que: Ax=b -> LUx=b -> Ly=b\n",
        "\n",
        "    # Se resuelve Ly=b\n",
        "    y = L.gauss_jordan_solve(b)[0] #Solucion del sistema Ly = b\n",
        "\n",
        "    # Se resuelve Ux=y\n",
        "    x = U.gauss_jordan_solve(y)[0] #Solucion del sistema Ux = y\n",
        "\n",
        "    return x\n",
        "\n",
        "  #Se construye el spline cúbico S con sus respectivos S_j.\n",
        "  #Retorna a_j, b_j, c_j y d_j.\n",
        "  def construir_spline_cubico(self):\n",
        "    self.c = self.resolver_sistema_lineal()\n",
        "    \n",
        "    #coeficiente b\n",
        "    for i in range(self.n-1):\n",
        "      self.b[i] = (self.a[i+1] - self.a[i])/self.h[i] - self.h[i]*(2*self.c[i] + self.c[i+1])/3  \n",
        "\n",
        "    #coeficiente d\n",
        "    for i in range(self.n-1):\n",
        "      self.d[i] = (self.c[i+1] - self.c[i])/(3*self.h[i])  \n",
        "\n",
        "    return self.a, self.b, self.c, self.d\n",
        "\n",
        "  #A partir de un \"j\", se obtiene \"S_j\".\n",
        "  def obtener_Sj(self, j):\n",
        "    a_j , b_j, c_j, d_j , x_j = self.obtener_parametros_Sj(j)\n",
        "\n",
        "    return '''S{j}(x) = ({a_j}) + ({b_j})(x-{x_j}) + ({c_j})(x-{x_j})^2 + ({d_j})(x-{x_j})^3'''.format(j=j, a_j=a_j, b_j= b_j, c_j=c_j,d_j=d_j,x_j=x_j)\n",
        "\n",
        "  #A partir de un \"j\", se obtienen a_j, b_j, c_j y d_j.\n",
        "  def obtener_parametros_Sj(self,j):\n",
        "    return self.a[j], self.b[j], self.c[j], self.d[j], self.x[j]\n",
        "\n",
        "  def obtener_todos_los_Sj(self):\n",
        "    for i in range(self.n-1):\n",
        "      display(polinomio.obtener_Sj(i)) "
      ],
      "metadata": {
        "id": "qTGgA-pE1vQm"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### $\\textrm{Implementacion - Forma 2}$\n",
        "\n",
        "A partir de la bibliografía de la materia, se propone otra forma de construir un Spline Cúbico."
      ],
      "metadata": {
        "id": "J0yZHPncJ8R5"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Esta otra implementación se utiliza de igual manera que la forma propuesta anteriormente.\n",
        "\n",
        "Se cuenta con la clase **SplineCubicoInterpolador**, la cual se inicializa con $4$ valores:\n",
        "- $nodos:$ la coordenada \"$x$\" de los puntos a interpolar.\n",
        "- $imagen\\_nodos:$ la coordenada \"$y$\" de los puntos a interpolar.\n",
        "- $fpo:$ la derivada primera de $f(x_0)$.\n",
        "- $fpn:$ la derivada primera de $f(x_n)$. \n",
        "\n",
        "Para generar el spline, se llama al método $construir\\_spline\\_cubico()$. Éste devuelve los coeficientes $a$, $b$, $c$ y $d$.\n",
        "\n",
        "En caso de querer visualizar los $S_j$, se invoca el método $obtener\\_Sj$ enviándole como parámetro el _j_ a utilizar.\n",
        "\n",
        "Y finalmente, en caso de querer visualizar todos los $S_j$, se utiliza el método $obtener\\_todos\\_los\\_Sj().$"
      ],
      "metadata": {
        "id": "DhpTKoqJSU6W"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "class SplineCubicoInterpolador():\n",
        "  \n",
        "  #Se inicializa un interpolador cuyos atributos son:\n",
        "  # • nodos: la coordenada \"x\" de los puntos a interpolar.\n",
        "  # • imagen_nodos: la coordenada \"y\" de los puntos a interpolar.\n",
        "  # • fpo: la derivada primera de f(x0).\n",
        "  # • fpn: la derivada primera de f(xn).\n",
        "  def __init__(self, nodos, imagen_nodos, fpo, fpn):\n",
        "\n",
        "    self.coef_a = imagen_nodos\n",
        "    self.nodos = nodos\n",
        "    self.n = len(nodos)\n",
        "\n",
        "    self.fpo = fpo\n",
        "    self.fpn = fpn\n",
        "\n",
        "    self.coef_b = [None] * (self.n-1)\n",
        "    self.coef_c = [None] * (self.n)\n",
        "    self.coef_d = [None] * (self.n-1)\n",
        "\n",
        "  #Se construye el spline cúbico S con sus respectivos S_j.\n",
        "  #Retorna a_j, b_j, c_j y d_j.\n",
        "  def construir_spline_cubico(self):\n",
        "\n",
        "    h = [None] * (self.n-1)\n",
        "    alpha = [None] * (self.n)\n",
        "\n",
        "    # Sistema lineal tridiagonal\n",
        "    l = [None] * (self.n)\n",
        "    mu = [None] * (self.n)\n",
        "    z = [None] * (self.n)\n",
        "\n",
        "    # Paso 1: se definen los h_i = x_{i+1} - x_i para facilitar los cálculos\n",
        "    for i in range(0,self.n-1):\n",
        "      h[i] = self.nodos[i+1] - self.nodos[i]\n",
        "\n",
        "    # Paso 2: se definen los α usando las derivadas\n",
        "    alpha[0] = (3*(self.coef_a[1] - self.coef_a[0]))/h[0] - (3*self.fpo)\n",
        "    alpha[self.n-1] = (3*self.fpn) - (3*(self.coef_a[len(self.coef_a)-1] - self.coef_a[len(self.coef_a)-2]))/h[len(h)-1]\n",
        "    \n",
        "    # Paso 3: se definen el resto de α\n",
        "    for i in range(1, self.n-1):\n",
        "      alpha[i] = (3*(self.coef_a[i+1] - self.coef_a[i]) / h[i]) - (3*(self.coef_a[i] - self.coef_a[i-1]) / h[i-1])\n",
        "\n",
        "    #Se resuelve el sistema lineal tridiagonal utilizando la factorización de Crout\n",
        "    # Paso 4: \n",
        "    l[0] = 2*h[0]\n",
        "    mu[0] = 0.5\n",
        "    z[0] = alpha[0]/l[0]\n",
        "\n",
        "    # Paso 5\n",
        "    for i in range(1,self.n-1):\n",
        "      l[i] = 2*(self.nodos[i+1] - self.nodos[i-1]) - (h[i-1]*mu[i-1])\n",
        "      mu[i] = h[i]/l[i]\n",
        "      z[i] = (alpha[i]-h[i-1]*z[i-1])/l[i]\n",
        "\n",
        "    # Paso 6\n",
        "    l[len(l)-1] = h[len(h)-1]*(2 - mu[len(mu)-2])\n",
        "    z[len(z)-1] = (alpha[len(alpha)-1] - h[len(h)-1]*z[len(z)-2])/l[len(l)-1]\n",
        "    self.coef_c[len(self.coef_c)-1] = z[len(z)-1]\n",
        "\n",
        "    # Paso 7\n",
        "    for i in range(self.n-2, 0-1, -1):\n",
        "      self.coef_c[i] = z[i] - (mu[i]*self.coef_c[i+1])\n",
        "      self.coef_b[i] = (self.coef_a[i+1] - self.coef_a[i])/h[i] - (h[i]*(self.coef_c[i+1] + 2*self.coef_c[i])/3)\n",
        "      self.coef_d[i] = (self.coef_c[i+1] - self.coef_c[i])/(3*h[i])\n",
        "\n",
        "    return [self.coef_a, self.coef_b, self.coef_c, self.coef_d]\n",
        "\n",
        "  #A partir de un \"j\", se obtiene \"S_j\".\n",
        "  def obtener_Sj(self, j):\n",
        "    a_j , b_j, c_j, d_j , x_j = self.obtener_parametros_Sj(j)\n",
        "\n",
        "    return '''S{j}(x) = ({a_j}) + ({b_j})(x-{x_j}) + ({c_j})(x-{x_j})^2 + ({d_j})(x-{x_j})^3'''.format(j=j, a_j=a_j, b_j= b_j, c_j=c_j,d_j=d_j,x_j=x_j)\n",
        "\n",
        "  #A partir de un \"j\", se obtienen a_j, b_j, c_j y d_j.\n",
        "  def obtener_parametros_Sj(self,j):\n",
        "    return self.coef_a[j], self.coef_b[j], self.coef_c[j], self.coef_d[j], self.nodos[j]\n",
        "\n",
        "  def obtener_todos_los_Sj(self):\n",
        "    for i in range(self.n-1):\n",
        "      display(polinomio.obtener_Sj(i)) "
      ],
      "metadata": {
        "id": "wV1tJ4SmA3Zd"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### $\\quad$**d)** $\\textrm{Interpolar los datos de la tabla 1 utilizando una Spline con frontera ligada.}$ $\\textrm{Mostrar los resultados en una tabla, donde las filas sean la i-esima spline }$ $\\textrm{y las columnas los coeficientes } a_i, b_i, c_i, d_i.$  "
      ],
      "metadata": {
        "id": "QvJ7noLvQzAu"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### $\\textrm{Informacion Inicial}$"
      ],
      "metadata": {
        "id": "2cnEtYW-9Pl3"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Para interpolar las $3$ curvas brindadas por el enunciado, se utilizarán $3$ splines.\n",
        "\n",
        "- La primera curva comienza en $x = 1$, con un valor de $3.0$, y termina en $x = 17$ con un valor de $4.5$.\n",
        "- La segunda curva comienza en $x = 17$, con un valor de $4.5$, y termina en $x = 27.7$ con un valor de $4.1$.\n",
        "- La tercera curva comienza en $x = 27.7$, con un valor de $4.1$, y termina en $x = 30$ con un valor de $3.0$.\n",
        "\n",
        "Para plantear Spline, no solo se necesitan los valores de $x$ y $f(x)$, sino que también de las derivadas. A partir del gráfico se sabe que:\n",
        "- Las derivadas primeras del extremo izquierdo y derecho de la primera curva valen $1$ y $-\\frac23$ respectivamente.\n",
        "- Las derivadas primeras del extremo izquierdo y derecho de la segunda curva valen $3$ y $-4$ respectivamente.\n",
        "- Las derivadas primeras del extremo izquierdo y derecho de la tercera curva valen $\\frac13$ y $-\\frac32$ respectivamente.\n",
        "\n",
        "A su vez, el enunciado brinda información sobre algunos puntos de cada curva.Para construir cada spline, se tendrán polinomios cúbicos, cada uno en el subintervalo $\\begin{bmatrix}x_j, & x_{j+1}\\end{bmatrix}$ para cada $j = 0, 1, \\dots, n - 1$, de la forma\n",
        "$$S_j(x) = a_j + b_j (x - x_j) + c_j(x-x_j) + d_j(x-x_j).$$ Es decir, un $S_j$ entre cada par de puntos.\n",
        "- Se cuenta con las coordenadas de $9$ puntos de la primera curva, por lo que el primer spline estará compuesto por $8$ tramos $\\{S_j\\}_{j=0}^7$.\n",
        "- Se cuenta con las coordenadas de $7$ puntos de la primera curva, por lo que el segundo spline estará compuesto por $6$ tramos $\\{S_j\\}_{j=0}^5$.\n",
        "- Se cuenta con las coordenadas de $4$ puntos de la primera curva, por lo que el tercer spline estará compuesto por $3$ tramos $\\{S_j\\}_{j=0}^2$."
      ],
      "metadata": {
        "id": "owj0AKkBsUN4"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Finalmente, nuestros datos son:\n",
        "\n",
        "**Datos**\n",
        "> **Curva 1**\n",
        ">\\begin{aligned}\n",
        "&\\bullet \\quad x_0 = 1 &&\\bullet \\quad f(x_0) = 3.0 &&\\bullet \\quad f'(x_0) = 1,\\\\\n",
        "&\\bullet \\quad x_1 = 2 &&\\bullet \\quad f(x_1) = 3.7,\\\\\n",
        "&\\bullet \\quad x_2 = 5 &&\\bullet \\quad f(x_2) = 3.9,\\\\\n",
        "&\\bullet \\quad x_3 = 6 &&\\bullet \\quad f(x_3) = 4.2,\\\\\n",
        "&\\bullet \\quad x_4 = 7 &&\\bullet \\quad f(x_4) = 5.7,\\\\\n",
        "&\\bullet \\quad x_5 = 8 &&\\bullet \\quad f(x_5) = 6.6,\\\\\n",
        "&\\bullet \\quad x_6 = 10 &&\\bullet \\quad f(x_6) = 7.1,\\\\\n",
        "&\\bullet \\quad x_7 = 13 &&\\bullet \\quad f(x_7) = 6.7,\\\\\n",
        "&\\bullet \\quad x_8 = 17\\quad &&\\bullet \\quad f(x_8) = 4.5 &&\\bullet \\quad f'(x_8) = -0.666666667.\\\\\n",
        "\\end{aligned}\n",
        "\n",
        "> **Curva 2**\n",
        ">\\begin{aligned}\n",
        "&\\bullet \\quad x_0 = 17 &&\\bullet \\quad f(x_0) = 4.5 &&\\bullet \\quad f'(x_0) = 3,\\\\\n",
        "&\\bullet \\quad x_1 = 20 &&\\bullet \\quad f(x_1) = 7.0,\\\\\n",
        "&\\bullet \\quad x_2 = 23 &&\\bullet \\quad f(x_2) = 6.1,\\\\\n",
        "&\\bullet \\quad x_3 = 24 &&\\bullet \\quad f(x_3) = 5.6,\\\\\n",
        "&\\bullet \\quad x_4 = 25 &&\\bullet \\quad f(x_4) = 5.8,\\\\\n",
        "&\\bullet \\quad x_5 = 27 &&\\bullet \\quad f(x_5) = 5.2,\\\\\n",
        "&\\bullet \\quad x_6 = 27.7 &&\\bullet \\quad f(x_6) = 4.1 &&\\bullet \\quad f'(x_6) = -4.\\quad\\quad\\quad\\quad\\\\\n",
        "\\end{aligned}\n",
        "\n",
        "> **Curva 3**\n",
        ">\\begin{aligned}\n",
        "&\\bullet \\quad x_0 = 27.7 &&\\bullet \\quad f(x_0) = 4.1 &&\\bullet \\quad f'(x_0) = 0.333333333\\\\\n",
        "&\\bullet \\quad x_1 = 28 &&\\bullet \\quad f(x_1) = 4.3,\\\\\n",
        "&\\bullet \\quad x_2 = 29 &&\\bullet \\quad f(x_2) = 4.1,\\\\\n",
        "&\\bullet \\quad x_3 = 30 &&\\bullet \\quad f(x_3) = 3.0 &&\\bullet \\quad f'(x_3) = -1.5.\\\\\n",
        "\\end{aligned}\n"
      ],
      "metadata": {
        "id": "o9E3O_kLPiag"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### $\\textrm{Obtencion de los Splines Cubicos}$\n",
        "\n",
        "Estos Splines cúbicos pueden obtenerse a partir del código implementado en el item **($c$)**.\n",
        "\n",
        "Sin embargo, se decide obtener los Splines paso a paso para poder visualizar mejor lo que está sucediendo en cada uno."
      ],
      "metadata": {
        "id": "ZgVaWUXdbyBJ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Pasos**\n",
        "\n",
        "$\\quad i.\\quad$ **Resolución Sistema Lineal**: A partir de la conclusión alcanzada en el item **($b$)**, se arman las matrices $A$ y $b$ para cada curva. Luego, se resuelven los sistemas lineales $Ax = b$ mediante la **factorización** $LU$ donde $x$ es el coeficiente $c$.\n",
        "\n",
        "$\\quad ii.\\quad$ **Cálculo de coeficientes $b$ y $d$**: De acuerdo con el valor del coeficiente $c$ obtenido al resolver el sistema lineal, se calculan los coeficientes $b$ y $d$.\n",
        "\n",
        "- Los $b_j$ se calculan con lo despejado en **($6$)**:\n",
        "$$b_j = \\frac{a_{j+1}-a_j}{x_{j+1}-x_j} - \\frac{(x_{j+1}-x_j)(2c_j + c_{j+1})}{3}$$\n",
        "- Los $d_j$ se calculan a partir de\n",
        "$$d_j = \\frac{(c_{j+1} - c_j)}{3(x_{j+1}-x_j)}$$\n",
        "\n",
        "$\\quad iii.\\quad$ **Tabla con los datos obtenidos**: Por último se pueden visualizar los datos obtenidos mediante una tabla.\n"
      ],
      "metadata": {
        "id": "wt87AQrel75D"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sympy import *\n",
        "init_printing(use_unicode=True)\n",
        "import numpy as np\n",
        "from tabulate import tabulate"
      ],
      "metadata": {
        "id": "JFSu99NcdeEQ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "##### $\\textrm{Curva } 1$"
      ],
      "metadata": {
        "id": "8_PtxvBRdfP-"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Se escriben los datos, y se calculan los ($x_{j+1} - x_j$), los cuales se denotarán como $h_j$ para facilitar la lectura."
      ],
      "metadata": {
        "id": "BmG02HnPkJ9B"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#Datos\n",
        "x_curva1 = [1,2,5,6,7,8,10,13,17]\n",
        "a_curva1 = [3.0,3.7,3.9,4.2,5.7,6.6,7.1,6.7,4.5]\n",
        "fp0_curva1 = 1\n",
        "fpn_curva1 = -0.666666667\n",
        "tope = len(x_curva1) - 1\n",
        "\n",
        "#para facilitar notacion h_j = x_{j+1} - x_j\n",
        "h = [None] * (tope)\n",
        "for i in range(tope):\n",
        "  h[i] = x_curva1[i+1] - x_curva1[i]"
      ],
      "metadata": {
        "id": "jGkIamJ6kJfu"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "###### $\\textrm{Resolucion Sistema Lineal}$\n"
      ],
      "metadata": {
        "id": "sLoumoMb9WFb"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Se construye la matriz $A$"
      ],
      "metadata": {
        "id": "idEuvHr_kciq"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#Matriz de 0s\n",
        "A = zeros(tope + 1)\n",
        "\n",
        "#Primera fila\n",
        "A[0,0] = 2*h[0]\n",
        "A[0,1] = h[0]\n",
        "\n",
        "#Resto de filas menos la última\n",
        "for i in range(tope-1):\n",
        "  A[i+1,i] = h[i]\n",
        "  A[i+1,i+1] = 2*(h[i]+h[i+1])\n",
        "  A[i+1,i+2] = h[i+1]\n",
        "\n",
        "#Ultima fila\n",
        "A[tope, tope-1] = h[tope-1]\n",
        "A[tope, tope] = 2*h[tope-1]\n",
        "\n",
        "display(A)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 200
        },
        "id": "nBU-5RfJYX07",
        "outputId": "050693be-230e-4869-b760-9317411ac9c8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "⎡2  1  0  0  0  0  0   0   0⎤\n",
              "⎢                           ⎥\n",
              "⎢1  8  3  0  0  0  0   0   0⎥\n",
              "⎢                           ⎥\n",
              "⎢0  3  8  1  0  0  0   0   0⎥\n",
              "⎢                           ⎥\n",
              "⎢0  0  1  4  1  0  0   0   0⎥\n",
              "⎢                           ⎥\n",
              "⎢0  0  0  1  4  1  0   0   0⎥\n",
              "⎢                           ⎥\n",
              "⎢0  0  0  0  1  6  2   0   0⎥\n",
              "⎢                           ⎥\n",
              "⎢0  0  0  0  0  2  10  3   0⎥\n",
              "⎢                           ⎥\n",
              "⎢0  0  0  0  0  0  3   14  4⎥\n",
              "⎢                           ⎥\n",
              "⎣0  0  0  0  0  0  0   4   8⎦"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}2 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\1 & 8 & 3 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 3 & 8 & 1 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 1 & 4 & 1 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 1 & 4 & 1 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 1 & 6 & 2 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 2 & 10 & 3 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 3 & 14 & 4\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 4 & 8\\end{matrix}\\right]$"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Se construye la matriz $b$"
      ],
      "metadata": {
        "id": "mJk2q7mSkkY7"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "b = Matrix([3*(a_curva1[1]-a_curva1[0])/h[0] - 3*fp0_curva1])\n",
        "for i in range(tope-1):\n",
        "  b = Matrix.vstack(b, Matrix([3*(a_curva1[i+2]-a_curva1[i+1])/h[i+1] - 3*(a_curva1[i+1]-a_curva1[i])/h[i]]))\n",
        "b = Matrix.vstack(b, Matrix([3*fpn_curva1 - 3*(a_curva1[tope]-a_curva1[tope-1])/h[tope-1]]))\n",
        "\n",
        "display(b)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 200
        },
        "id": "NgwJH_hSklCn",
        "outputId": "55c319ac-ab2c-4afb-ac1d-7e198aed641d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "⎡-0.899999999999999⎤\n",
              "⎢                  ⎥\n",
              "⎢       -1.9       ⎥\n",
              "⎢                  ⎥\n",
              "⎢0.700000000000001 ⎥\n",
              "⎢                  ⎥\n",
              "⎢       3.6        ⎥\n",
              "⎢                  ⎥\n",
              "⎢       -1.8       ⎥\n",
              "⎢                  ⎥\n",
              "⎢      -1.95       ⎥\n",
              "⎢                  ⎥\n",
              "⎢      -1.15       ⎥\n",
              "⎢                  ⎥\n",
              "⎢      -1.25       ⎥\n",
              "⎢                  ⎥\n",
              "⎣   -0.350000001   ⎦"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}-0.899999999999999\\\\-1.9\\\\0.700000000000001\\\\3.6\\\\-1.8\\\\-1.95\\\\-1.15\\\\-1.25\\\\-0.350000001\\end{matrix}\\right]$"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Y finalmente se resuelve el sistema lineal $Ax = b$ mediante la **factorización $LU$**."
      ],
      "metadata": {
        "id": "2jixaQndkqDR"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "A_copia = np.array(A.copy().tolist())\n",
        "n = A_copia.shape[0]\n",
        "U = A_copia.copy()\n",
        "L = np.eye(n, dtype=np.double)\n",
        "\n",
        "for i in range(n):\n",
        "    factor = U[i+1:, i] / U[i, i]\n",
        "    L[i+1:, i] = factor\n",
        "    U[i+1:] -= factor[:, np.newaxis] * U[i]\n",
        "\n",
        "#se obtiene matriz triangular inferior        \n",
        "L = Matrix(L)\n",
        "#se obtiene matriz triangular superior        \n",
        "U = Matrix(U)\n",
        "\n",
        "# Se sabe que: Ax=b -> LUx=b -> Ly=b\n",
        "\n",
        "# Se resuelve Ly=b\n",
        "y = L.gauss_jordan_solve(b)[0] #Solucion del sistema Ly = b\n",
        "\n",
        "# Se resuelve Ux=y\n",
        "c_curva1 = U.gauss_jordan_solve(y)[0] #Solucion del sistema Ux = y\n",
        "\n",
        "display(c_curva1)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 200
        },
        "id": "9V1sRIyix6Tk",
        "outputId": "7eb86eb1-5de7-4ae2-9f56-bb844d89c06a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "⎡ -0.346809861280228 ⎤\n",
              "⎢                    ⎥\n",
              "⎢ -0.206380277439543 ⎥\n",
              "⎢                    ⎥\n",
              "⎢ 0.0326173602655243 ⎥\n",
              "⎢                    ⎥\n",
              "⎢  1.05820195019444  ⎥\n",
              "⎢                    ⎥\n",
              "⎢ -0.665425161043271 ⎥\n",
              "⎢                    ⎥\n",
              "⎢ -0.196501306021354 ⎥\n",
              "⎢                    ⎥\n",
              "⎢-0.0527835014143018 ⎥\n",
              "⎢                    ⎥\n",
              "⎢-0.0763874579380913 ⎥\n",
              "⎢                    ⎥\n",
              "⎣-0.00555627115595435⎦"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}-0.346809861280228\\\\-0.206380277439543\\\\0.0326173602655243\\\\1.05820195019444\\\\-0.665425161043271\\\\-0.196501306021354\\\\-0.0527835014143018\\\\-0.0763874579380913\\\\-0.00555627115595435\\end{matrix}\\right]$"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "###### $\\textrm{Calculo de coeficientes } b \\textrm{ y } d$\n"
      ],
      "metadata": {
        "id": "lP0hnYVgml6w"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Coeficiente $b:$"
      ],
      "metadata": {
        "id": "BCZmb0yLNg4K"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "b_curva1 = [None] * tope\n",
        "for i in range(tope):\n",
        "  b_curva1[i] = (a_curva1[i+1] - a_curva1[i])/h[i] - h[i]*(2*c_curva1[i] + c_curva1[i+1])/3  \n",
        "\n",
        "display(b_curva1)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ZE1zSznHOneR",
        "outputId": "4fd6de83-dd52-4bac-8dd1-f9212a3dd03c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "[1.0, 0.446809861280229, -0.074478890241828, 1.01634042021813, 1.4091172093693\n",
              ", 0.547190742304673, 0.0486211274333617, -0.338891750623817]"
            ],
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\left[ 1.0, \\  0.446809861280229, \\  -0.074478890241828, \\  1.01634042021813, \\  1.4091172093693, \\  0.547190742304673, \\  0.0486211274333617, \\  -0.338891750623817\\right]$"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Coeficiente $d:$"
      ],
      "metadata": {
        "id": "hnIsFRVmn88o"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "d_curva1 = [None] * tope\n",
        "for i in range(tope):\n",
        "  d_curva1[i] = (c_curva1[i+1] - c_curva1[i])/(3*h[i])  \n",
        "\n",
        "display(d_curva1)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1A3VrDdqPaKf",
        "outputId": "d38ffffa-577e-4d21-c2e5-b536e4a04cdc"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "[0.0468098612802284, 0.0265552930783408, 0.341861529976304, -0.574542370412569\n",
              ", 0.156307951673972, 0.0239529674345087, -0.00262266183597661, 0.0059025988985\n",
              "1141]"
            ],
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\left[ 0.0468098612802284, \\  0.0265552930783408, \\  0.341861529976304, \\  -0.574542370412569, \\  0.156307951673972, \\  0.0239529674345087, \\  -0.00262266183597661, \\  0.00590259889851141\\right]$"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "###### $\\textrm{Tabla con los datos obtenidos}$\n"
      ],
      "metadata": {
        "id": "gDxb6fxDo2q2"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "table = [['j', 'Sj(x)', 'aj', 'bj', 'cj', 'dj', 'Punto inicial', 'Punto final'],\n",
        "         *[[i, '''S{i}(x)'''.format(i=i), a_curva1[i], b_curva1[i], c_curva1[i], d_curva1[i],\n",
        "            '''({x}, {y})'''.format(x=x_curva1[i], y=a_curva1[i]),\n",
        "            '''({x}, {y})'''.format(x=x_curva1[i+1], y=a_curva1[i+1])]  for i in range(tope)]]\n",
        "\n",
        "print(tabulate(table, headers='firstrow', tablefmt='fancy_grid'))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tPBeZ8iRpj5H",
        "outputId": "45553aaa-9e8e-4825-f1a1-b546c75065f2"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "╒═════╤═════════╤══════╤════════════╤════════════╤═════════════╤═════════════════╤═══════════════╕\n",
            "│   j │ Sj(x)   │   aj │         bj │         cj │          dj │ Punto inicial   │ Punto final   │\n",
            "╞═════╪═════════╪══════╪════════════╪════════════╪═════════════╪═════════════════╪═══════════════╡\n",
            "│   0 │ S0(x)   │  3   │  1         │ -0.34681   │  0.0468099  │ (1, 3.0)        │ (2, 3.7)      │\n",
            "├─────┼─────────┼──────┼────────────┼────────────┼─────────────┼─────────────────┼───────────────┤\n",
            "│   1 │ S1(x)   │  3.7 │  0.44681   │ -0.20638   │  0.0265553  │ (2, 3.7)        │ (5, 3.9)      │\n",
            "├─────┼─────────┼──────┼────────────┼────────────┼─────────────┼─────────────────┼───────────────┤\n",
            "│   2 │ S2(x)   │  3.9 │ -0.0744789 │  0.0326174 │  0.341862   │ (5, 3.9)        │ (6, 4.2)      │\n",
            "├─────┼─────────┼──────┼────────────┼────────────┼─────────────┼─────────────────┼───────────────┤\n",
            "│   3 │ S3(x)   │  4.2 │  1.01634   │  1.0582    │ -0.574542   │ (6, 4.2)        │ (7, 5.7)      │\n",
            "├─────┼─────────┼──────┼────────────┼────────────┼─────────────┼─────────────────┼───────────────┤\n",
            "│   4 │ S4(x)   │  5.7 │  1.40912   │ -0.665425  │  0.156308   │ (7, 5.7)        │ (8, 6.6)      │\n",
            "├─────┼─────────┼──────┼────────────┼────────────┼─────────────┼─────────────────┼───────────────┤\n",
            "│   5 │ S5(x)   │  6.6 │  0.547191  │ -0.196501  │  0.023953   │ (8, 6.6)        │ (10, 7.1)     │\n",
            "├─────┼─────────┼──────┼────────────┼────────────┼─────────────┼─────────────────┼───────────────┤\n",
            "│   6 │ S6(x)   │  7.1 │  0.0486211 │ -0.0527835 │ -0.00262266 │ (10, 7.1)       │ (13, 6.7)     │\n",
            "├─────┼─────────┼──────┼────────────┼────────────┼─────────────┼─────────────────┼───────────────┤\n",
            "│   7 │ S7(x)   │  6.7 │ -0.338892  │ -0.0763875 │  0.0059026  │ (13, 6.7)       │ (17, 4.5)     │\n",
            "╘═════╧═════════╧══════╧════════════╧════════════╧═════════════╧═════════════════╧═══════════════╛\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Se puede ver que es exactamente el mismo Spline que se obtiene al utilizar el algoritmo implementado previamente."
      ],
      "metadata": {
        "id": "DeDAmpdDq8CG"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Primero se construye un spline con la implementación de la **forma 1:**"
      ],
      "metadata": {
        "id": "IGHOa22px8kV"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "polinomio = SplineCubico(x_curva1, a_curva1, fp0_curva1, fpn_curva1)\n",
        "polinomio.construir_spline_cubico()\n",
        "polinomio.obtener_todos_los_Sj()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 165
        },
        "id": "Li2fXO-Ty1WA",
        "outputId": "5f384c01-4264-40db-8898-c362053b3e39"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'S0(x) = (3.0) + (1.00000000000000)(x-1) + (-0.346809861280228)(x-1)^2 + (0.0468098612802284)(x-1)^3'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'S1(x) = (3.7) + (0.446809861280229)(x-2) + (-0.206380277439543)(x-2)^2 + (0.0265552930783408)(x-2)^3'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'S2(x) = (3.9) + (-0.0744788902418280)(x-5) + (0.0326173602655243)(x-5)^2 + (0.341861529976304)(x-5)^3'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'S3(x) = (4.2) + (1.01634042021813)(x-6) + (1.05820195019444)(x-6)^2 + (-0.574542370412569)(x-6)^3'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'S4(x) = (5.7) + (1.40911720936930)(x-7) + (-0.665425161043271)(x-7)^2 + (0.156307951673972)(x-7)^3'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'S5(x) = (6.6) + (0.547190742304673)(x-8) + (-0.196501306021354)(x-8)^2 + (0.0239529674345087)(x-8)^3'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'S6(x) = (7.1) + (0.0486211274333617)(x-10) + (-0.0527835014143018)(x-10)^2 + (-0.00262266183597661)(x-10)^3'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'S7(x) = (6.7) + (-0.338891750623817)(x-13) + (-0.0763874579380913)(x-13)^2 + (0.00590259889851141)(x-13)^3'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Y ahora con la implementación de la **forma 2:**"
      ],
      "metadata": {
        "id": "r4l-GnvnyAQ9"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "polinomio = SplineCubicoInterpolador(x_curva1, a_curva1, fp0_curva1, fpn_curva1)\n",
        "polinomio.construir_spline_cubico()\n",
        "polinomio.obtener_todos_los_Sj()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 165
        },
        "id": "IUH2l5EJx5Re",
        "outputId": "dd9c2fc9-8101-4989-dbe5-c6c907d4be48"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'S0(x) = (3.0) + (1.0)(x-1) + (-0.34680986128022817)(x-1)^2 + (0.04680986128022833)(x-1)^3'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'S1(x) = (3.7) + (0.44680986128022865)(x-2) + (-0.20638027743954318)(x-2)^2 + (0.02655529307834083)(x-2)^3'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'S2(x) = (3.9) + (-0.07447889024182808)(x-5) + (0.03261736026552431)(x-5)^2 + (0.3418615299763041)(x-5)^3'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'S3(x) = (4.2) + (1.0163404202181328)(x-6) + (1.0582019501944364)(x-6)^2 + (-0.5745423704125692)(x-6)^3'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'S4(x) = (5.7) + (1.409117209369298)(x-7) + (-0.6654251610432711)(x-7)^2 + (0.15630795167397238)(x-7)^3'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'S5(x) = (6.6) + (0.5471907423046731)(x-8) + (-0.196501306021354)(x-8)^2 + (0.023952967434508702)(x-8)^3'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'S6(x) = (7.1) + (0.048621127433361666)(x-10) + (-0.05278350141430177)(x-10)^2 + (-0.002622661835976612)(x-10)^3'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'S7(x) = (6.7) + (-0.3388917506238175)(x-13) + (-0.07638745793809128)(x-13)^2 + (0.0059025988985114105)(x-13)^3'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "##### $\\textrm{Curva } 2$"
      ],
      "metadata": {
        "id": "GPUtVXpnyecY"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Se escriben los datos, y se calculan los ($x_{j+1} - x_j$), los cuales se denotarán como $h_j$ para facilitar la lectura."
      ],
      "metadata": {
        "id": "61ZUk-gLyecZ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#Datos\n",
        "x_curva2 = [17,20,23,24,25,27,27.7]\n",
        "a_curva2 = [4.5,7.0,6.1,5.6,5.8,5.2,4.1]\n",
        "fp0_curva2 = 3\n",
        "fpn_curva2 = -4\n",
        "tope = len(x_curva2) - 1\n",
        "\n",
        "#para facilitar notacion h_j = x_{j+1} - x_j\n",
        "h = [None] * (tope)\n",
        "for i in range(tope):\n",
        "  h[i] = x_curva2[i+1] - x_curva2[i]"
      ],
      "metadata": {
        "id": "kBR-vHtFyeca"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "###### $\\textrm{Resolucion Sistema Lineal}$\n"
      ],
      "metadata": {
        "id": "OGoJm7ysyecc"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Se construye la matriz $A$"
      ],
      "metadata": {
        "id": "Q1P07QTgyecc"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#Matriz de 0s\n",
        "A = zeros(tope + 1)\n",
        "\n",
        "#Primera fila\n",
        "A[0,0] = 2*h[0]\n",
        "A[0,1] = h[0]\n",
        "\n",
        "#Resto de filas menos la última\n",
        "for i in range(tope-1):\n",
        "  A[i+1,i] = h[i]\n",
        "  A[i+1,i+1] = 2*(h[i]+h[i+1])\n",
        "  A[i+1,i+2] = h[i+1]\n",
        "\n",
        "#Ultima fila\n",
        "A[tope, tope-1] = h[tope-1]\n",
        "A[tope, tope] = 2*h[tope-1]\n",
        "\n",
        "display(A)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "865564c7-0248-482b-aed5-4fdf5ae75f44",
        "id": "4OX7HZsAyecd"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "⎡6  3   0  0  0          0                  0        ⎤\n",
              "⎢                                                    ⎥\n",
              "⎢3  12  3  0  0          0                  0        ⎥\n",
              "⎢                                                    ⎥\n",
              "⎢0  3   8  1  0          0                  0        ⎥\n",
              "⎢                                                    ⎥\n",
              "⎢0  0   1  4  1          0                  0        ⎥\n",
              "⎢                                                    ⎥\n",
              "⎢0  0   0  1  6          2                  0        ⎥\n",
              "⎢                                                    ⎥\n",
              "⎢0  0   0  0  2         5.4         0.699999999999999⎥\n",
              "⎢                                                    ⎥\n",
              "⎣0  0   0  0  0  0.699999999999999         1.4       ⎦"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}6 & 3 & 0 & 0 & 0 & 0 & 0\\\\3 & 12 & 3 & 0 & 0 & 0 & 0\\\\0 & 3 & 8 & 1 & 0 & 0 & 0\\\\0 & 0 & 1 & 4 & 1 & 0 & 0\\\\0 & 0 & 0 & 1 & 6 & 2 & 0\\\\0 & 0 & 0 & 0 & 2 & 5.4 & 0.699999999999999\\\\0 & 0 & 0 & 0 & 0 & 0.699999999999999 & 1.4\\end{matrix}\\right]$"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Se construye la matriz $b$"
      ],
      "metadata": {
        "id": "ubzChorFyecf"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "b = Matrix([3*(a_curva2[1]-a_curva2[0])/h[0] - 3*fp0_curva2])\n",
        "for i in range(tope-1):\n",
        "  b = Matrix.vstack(b, Matrix([3*(a_curva2[i+2]-a_curva2[i+1])/h[i+1] - 3*(a_curva2[i+1]-a_curva2[i])/h[i]]))\n",
        "b = Matrix.vstack(b, Matrix([3*fpn_curva2 - 3*(a_curva2[tope]-a_curva2[tope-1])/h[tope-1]]))\n",
        "\n",
        "display(b)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "941e8ce1-bcf1-43e4-9ae4-0e12c4c8aae1",
        "id": "D-NNS2gRyecf"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "⎡      -6.5       ⎤\n",
              "⎢                 ⎥\n",
              "⎢      -3.4       ⎥\n",
              "⎢                 ⎥\n",
              "⎢      -0.6       ⎥\n",
              "⎢                 ⎥\n",
              "⎢       2.1       ⎥\n",
              "⎢                 ⎥\n",
              "⎢      -1.5       ⎥\n",
              "⎢                 ⎥\n",
              "⎢-3.81428571428572⎥\n",
              "⎢                 ⎥\n",
              "⎣-7.28571428571428⎦"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}-6.5\\\\-3.4\\\\-0.6\\\\2.1\\\\-1.5\\\\-3.81428571428572\\\\-7.28571428571428\\end{matrix}\\right]$"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Y finalmente se resuelve el sistema lineal $Ax = b$ mediante la **factorización $LU$**."
      ],
      "metadata": {
        "id": "0vdQJ6y_yecg"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "A_copia = np.array(A.copy().tolist())\n",
        "n = A_copia.shape[0]\n",
        "U = A_copia.copy()\n",
        "L = np.eye(n, dtype=np.double)\n",
        "\n",
        "for i in range(n):\n",
        "    factor = U[i+1:, i] / U[i, i]\n",
        "    L[i+1:, i] = factor\n",
        "    U[i+1:] -= factor[:, np.newaxis] * U[i]\n",
        "\n",
        "#se obtiene matriz triangular inferior        \n",
        "L = Matrix(L)\n",
        "#se obtiene matriz triangular superior        \n",
        "U = Matrix(U)\n",
        "\n",
        "# Se sabe que: Ax=b -> LUx=b -> Ly=b\n",
        "\n",
        "# Se resuelve Ly=b\n",
        "y = L.gauss_jordan_solve(b)[0] #Solucion del sistema Ly = b\n",
        "\n",
        "# Se resuelve Ux=y\n",
        "c_curva2 = U.gauss_jordan_solve(y)[0] #Solucion del sistema Ux = y\n",
        "\n",
        "display(c_curva2)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "fe03c0bf-2e4f-4f80-800b-90713c2e780f",
        "id": "7m9qeeOEyech"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "⎡-1.10070845106297 ⎤\n",
              "⎢                  ⎥\n",
              "⎢0.0347502354592788⎥\n",
              "⎢                  ⎥\n",
              "⎢-0.171625824107476⎥\n",
              "⎢                  ⎥\n",
              "⎢0.668755886481972 ⎥\n",
              "⎢                  ⎥\n",
              "⎢-0.40339772182041 ⎥\n",
              "⎢                  ⎥\n",
              "⎢0.125815222220245 ⎥\n",
              "⎢                  ⎥\n",
              "⎣-5.26698924376318 ⎦"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}-1.10070845106297\\\\0.0347502354592788\\\\-0.171625824107476\\\\0.668755886481972\\\\-0.40339772182041\\\\0.125815222220245\\\\-5.26698924376318\\end{matrix}\\right]$"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "###### $\\textrm{Calculo de coeficientes } b \\textrm{ y } d$\n"
      ],
      "metadata": {
        "id": "U6mq1Wfoyecj"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Coeficiente $b:$"
      ],
      "metadata": {
        "id": "fChJLkWCyecl"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "b_curva2 = [None] * tope\n",
        "for i in range(tope):\n",
        "  b_curva2[i] = (a_curva2[i+1] - a_curva2[i])/h[i] - h[i]*(2*c_curva2[i] + c_curva2[i+1])/3  \n",
        "\n",
        "display(b_curva2)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e8ada2ed-ddcb-4f2f-c4e8-65071e7dd10a",
        "id": "wb2LjUHAyecn"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "[3.0, -0.197874646811082, -0.608501412755673, -0.111371350381178, 0.1539868142\n",
              "80384, -0.401178184919947]"
            ],
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\left[ 3.0, \\  -0.197874646811082, \\  -0.608501412755673, \\  -0.111371350381178, \\  0.153986814280384, \\  -0.401178184919947\\right]$"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Coeficiente $d:$"
      ],
      "metadata": {
        "id": "KOJBmGViyeco"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "d_curva2 = [None] * tope\n",
        "for i in range(tope):\n",
        "  d_curva2[i] = (c_curva2[i+1] - c_curva2[i])/(3*h[i])  \n",
        "\n",
        "display(d_curva2)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "5385377c-dc7f-4af4-96b9-db6a18644942",
        "id": "ilcueR3ryeco"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "[0.12616207628025, -0.022930673285195, 0.280127236863149, -0.357384536100794, \n",
              "0.0882021573401092, -2.56800212665878]"
            ],
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\left[ 0.12616207628025, \\  -0.022930673285195, \\  0.280127236863149, \\  -0.357384536100794, \\  0.0882021573401092, \\  -2.56800212665878\\right]$"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "###### $\\textrm{Tabla con los datos obtenidos}$\n"
      ],
      "metadata": {
        "id": "xpjGUJIqyecp"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "table = [['j', 'Sj(x)', 'aj', 'bj', 'cj', 'dj', 'Punto inicial', 'Punto final'],\n",
        "         *[[i, '''S{i}(x)'''.format(i=i),\n",
        "            np.format_float_positional(a_curva2[i]),\n",
        "            \"{:e}\".format(b_curva2[i]),\n",
        "            np.format_float_scientific(c_curva2[i]),\n",
        "            np.format_float_scientific(d_curva2[i]),\n",
        "            '''({x}, {y})'''.format(x=x_curva2[i], y=a_curva2[i]),\n",
        "            '''({x}, {y})'''.format(x=x_curva2[i+1], y=a_curva2[i+1])]  for i in range(tope)]]\n",
        "\n",
        "print(tabulate(table, headers='firstrow', tablefmt='fancy_grid'))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "6a7470b5-8739-45dc-e8c6-69a0ed053f59",
        "id": "80MvSzNDyecp"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "╒═════╤═════════╤══════╤═══════════╤════════════╤════════════╤═════════════════╤═══════════════╕\n",
            "│   j │ Sj(x)   │   aj │        bj │         cj │         dj │ Punto inicial   │ Punto final   │\n",
            "╞═════╪═════════╪══════╪═══════════╪════════════╪════════════╪═════════════════╪═══════════════╡\n",
            "│   0 │ S0(x)   │  4.5 │  3        │ -1.10071   │  0.126162  │ (17, 4.5)       │ (20, 7.0)     │\n",
            "├─────┼─────────┼──────┼───────────┼────────────┼────────────┼─────────────────┼───────────────┤\n",
            "│   1 │ S1(x)   │  7   │ -0.197875 │  0.0347502 │ -0.0229307 │ (20, 7.0)       │ (23, 6.1)     │\n",
            "├─────┼─────────┼──────┼───────────┼────────────┼────────────┼─────────────────┼───────────────┤\n",
            "│   2 │ S2(x)   │  6.1 │ -0.608501 │ -0.171626  │  0.280127  │ (23, 6.1)       │ (24, 5.6)     │\n",
            "├─────┼─────────┼──────┼───────────┼────────────┼────────────┼─────────────────┼───────────────┤\n",
            "│   3 │ S3(x)   │  5.6 │ -0.111371 │  0.668756  │ -0.357385  │ (24, 5.6)       │ (25, 5.8)     │\n",
            "├─────┼─────────┼──────┼───────────┼────────────┼────────────┼─────────────────┼───────────────┤\n",
            "│   4 │ S4(x)   │  5.8 │  0.153987 │ -0.403398  │  0.0882022 │ (25, 5.8)       │ (27, 5.2)     │\n",
            "├─────┼─────────┼──────┼───────────┼────────────┼────────────┼─────────────────┼───────────────┤\n",
            "│   5 │ S5(x)   │  5.2 │ -0.401178 │  0.125815  │ -2.568     │ (27, 5.2)       │ (27.7, 4.1)   │\n",
            "╘═════╧═════════╧══════╧═══════════╧════════════╧════════════╧═════════════════╧═══════════════╛\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Se puede ver que es exactamente el mismo Spline que se obtiene al utilizar el algoritmo implementado previamente."
      ],
      "metadata": {
        "id": "LEHJmRIvyecq"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "polinomio = SplineCubico(x_curva2, a_curva2, fp0_curva2, fpn_curva2)\n",
        "polinomio.construir_spline_cubico()\n",
        "polinomio.obtener_todos_los_Sj()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 128
        },
        "outputId": "c294e89f-b666-45e0-b7f3-d511db56e276",
        "id": "qWGIQ9Blyecr"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'S0(x) = (4.5) + (3.00000000000000)(x-17) + (-1.10070845106297)(x-17)^2 + (0.126162076280250)(x-17)^3'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'S1(x) = (7.0) + (-0.197874646811082)(x-20) + (0.0347502354592788)(x-20)^2 + (-0.0229306732851950)(x-20)^3'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'S2(x) = (6.1) + (-0.608501412755673)(x-23) + (-0.171625824107476)(x-23)^2 + (0.280127236863149)(x-23)^3'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'S3(x) = (5.6) + (-0.111371350381178)(x-24) + (0.668755886481972)(x-24)^2 + (-0.357384536100794)(x-24)^3'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'S4(x) = (5.8) + (0.153986814280384)(x-25) + (-0.403397721820410)(x-25)^2 + (0.0882021573401092)(x-25)^3'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'S5(x) = (5.2) + (-0.401178184919947)(x-27) + (0.125815222220245)(x-27)^2 + (-2.56800212665878)(x-27)^3'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "##### $\\textrm{Curva } 3$"
      ],
      "metadata": {
        "id": "wZ3rh6Tj3l8O"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Se escriben los datos, y se calculan los ($x_{j+1} - x_j$), los cuales se denotarán como $h_j$ para facilitar la lectura."
      ],
      "metadata": {
        "id": "XGRgaz5v3l8O"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#Datos\n",
        "x_curva3 = [27.7,28,29,30]\n",
        "a_curva3 = [4.1,4.3,4.1,3.0]\n",
        "fp0_curva3 = 0.333333333\n",
        "fpn_curva3 = -1.5\n",
        "tope = len(x_curva3) - 1\n",
        "\n",
        "#para facilitar notacion h_j = x_{j+1} - x_j\n",
        "h = [None] * (tope)\n",
        "for i in range(tope):\n",
        "  h[i] = x_curva3[i+1] - x_curva3[i]"
      ],
      "metadata": {
        "id": "E6y4jpxB3l8P"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "###### $\\textrm{Resolucion Sistema Lineal}$\n"
      ],
      "metadata": {
        "id": "GC5u6wZS3l8P"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Se construye la matriz $A$"
      ],
      "metadata": {
        "id": "AQfHYBvM3l8P"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#Matriz de 0s\n",
        "A = zeros(tope + 1)\n",
        "\n",
        "#Primera fila\n",
        "A[0,0] = 2*h[0]\n",
        "A[0,1] = h[0]\n",
        "\n",
        "#Resto de filas menos la última\n",
        "for i in range(tope-1):\n",
        "  A[i+1,i] = h[i]\n",
        "  A[i+1,i+1] = 2*(h[i]+h[i+1])\n",
        "  A[i+1,i+2] = h[i+1]\n",
        "\n",
        "#Ultima fila\n",
        "A[tope, tope-1] = h[tope-1]\n",
        "A[tope, tope] = 2*h[tope-1]\n",
        "\n",
        "display(A)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "6f62567f-70b6-4f7b-d7ad-9739e2c285cc",
        "id": "1lQ9rM3W3l8P"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "⎡0.600000000000001  0.300000000000001  0  0⎤\n",
              "⎢                                          ⎥\n",
              "⎢0.300000000000001         2.6         1  0⎥\n",
              "⎢                                          ⎥\n",
              "⎢        0                  1          4  1⎥\n",
              "⎢                                          ⎥\n",
              "⎣        0                  0          1  2⎦"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}0.600000000000001 & 0.300000000000001 & 0 & 0\\\\0.300000000000001 & 2.6 & 1 & 0\\\\0 & 1 & 4 & 1\\\\0 & 0 & 1 & 2\\end{matrix}\\right]$"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Se construye la matriz $b$"
      ],
      "metadata": {
        "id": "pAKq2sI-3l8Q"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "b = Matrix([3*(a_curva3[1]-a_curva3[0])/h[0] - 3*fp0_curva3])\n",
        "for i in range(tope-1):\n",
        "  b = Matrix.vstack(b, Matrix([3*(a_curva3[i+2]-a_curva3[i+1])/h[i+1] - 3*(a_curva3[i+1]-a_curva3[i])/h[i]]))\n",
        "b = Matrix.vstack(b, Matrix([3*fpn_curva3 - 3*(a_curva3[tope]-a_curva3[tope-1])/h[tope-1]]))\n",
        "\n",
        "display(b)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ea0819bf-496e-4eeb-bbdf-92ebc449122d",
        "id": "0pO-6U3l3l8Q"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "⎡1.000000001⎤\n",
              "⎢           ⎥\n",
              "⎢   -2.6    ⎥\n",
              "⎢           ⎥\n",
              "⎢   -2.7    ⎥\n",
              "⎢           ⎥\n",
              "⎣   -1.2    ⎦"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}1.000000001\\\\-2.6\\\\-2.7\\\\-1.2\\end{matrix}\\right]$"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Y finalmente se resuelve el sistema lineal $Ax = b$ mediante la **factorización $LU$**."
      ],
      "metadata": {
        "id": "PnfvSty53l8Q"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "A_copia = np.array(A.copy().tolist())\n",
        "n = A_copia.shape[0]\n",
        "U = A_copia.copy()\n",
        "L = np.eye(n, dtype=np.double)\n",
        "\n",
        "for i in range(n):\n",
        "    factor = U[i+1:, i] / U[i, i]\n",
        "    L[i+1:, i] = factor\n",
        "    U[i+1:] -= factor[:, np.newaxis] * U[i]\n",
        "\n",
        "#se obtiene matriz triangular inferior        \n",
        "L = Matrix(L)\n",
        "#se obtiene matriz triangular superior        \n",
        "U = Matrix(U)\n",
        "\n",
        "# Se sabe que: Ax=b -> LUx=b -> Ly=b\n",
        "\n",
        "# Se resuelve Ly=b\n",
        "y = L.gauss_jordan_solve(b)[0] #Solucion del sistema Ly = b\n",
        "\n",
        "# Se resuelve Ux=y\n",
        "c_curva3 = U.gauss_jordan_solve(y)[0] #Solucion del sistema Ux = y\n",
        "\n",
        "display(c_curva3)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "a64889bc-5e99-4381-cdc8-cd82fc5d296e",
        "id": "LIEaCCIt3l8Q"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "⎡ 2.24422442422441 ⎤\n",
              "⎢                  ⎥\n",
              "⎢-1.15511551178218 ⎥\n",
              "⎢                  ⎥\n",
              "⎢-0.269966996633663⎥\n",
              "⎢                  ⎥\n",
              "⎣-0.465016501683169⎦"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}2.24422442422441\\\\-1.15511551178218\\\\-0.269966996633663\\\\-0.465016501683169\\end{matrix}\\right]$"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "###### $\\textrm{Calculo de coeficientes } b \\textrm{ y } d$\n"
      ],
      "metadata": {
        "id": "pWjEaGOI3l8Q"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Coeficiente $b:$"
      ],
      "metadata": {
        "id": "asePNgyx3l8R"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "b_curva3 = [None] * tope\n",
        "for i in range(tope):\n",
        "  b_curva3[i] = (a_curva3[i+1] - a_curva3[i])/h[i] - h[i]*(2*c_curva3[i] + c_curva3[i+1])/3  \n",
        "\n",
        "display(b_curva3)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "48cc8162-270a-4938-bd85-c1fd6e621383",
        "id": "ZfBTlZNu3l8R"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "[0.333333333, 0.660066006732671, -0.765016501683168]"
            ],
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\left[ 0.333333333, \\  0.660066006732671, \\  -0.765016501683168\\right]$"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Coeficiente $d:$"
      ],
      "metadata": {
        "id": "FVXAI9bB3l8R"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "d_curva3 = [None] * tope\n",
        "for i in range(tope):\n",
        "  d_curva3[i] = (c_curva3[i+1] - c_curva3[i])/(3*h[i])  \n",
        "\n",
        "display(d_curva3)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "fa2f485e-7fb0-48a7-85c9-7733cd46fa52",
        "id": "2Sbj0GWH3l8R"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "[-3.77704437334064, 0.295049505049504, -0.0650165016831685]"
            ],
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\left[ -3.77704437334064, \\  0.295049505049504, \\  -0.0650165016831685\\right]$"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "###### $\\textrm{Tabla con los datos obtenidos}$\n"
      ],
      "metadata": {
        "id": "ikv50_Ho3l8R"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "table = [['j', 'Sj(x)', 'aj', 'bj', 'cj', 'dj', 'Punto inicial', 'Punto final'],\n",
        "         *[[i, '''S{i}(x)'''.format(i=i), a_curva3[i], b_curva3[i], c_curva3[i], d_curva3[i],\n",
        "            '''({x}, {y})'''.format(x=x_curva3[i], y=a_curva3[i]),\n",
        "            '''({x}, {y})'''.format(x=x_curva3[i+1], y=a_curva3[i+1])]  for i in range(tope)]]\n",
        "\n",
        "print(tabulate(table, headers='firstrow', tablefmt='fancy_grid'))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f6d29b91-d70c-4d75-dbbd-6dd9fe0a60da",
        "id": "g8-ey5d13l8R"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "╒═════╤═════════╤══════╤═══════════╤═══════════╤════════════╤═════════════════╤═══════════════╕\n",
            "│   j │ Sj(x)   │   aj │        bj │        cj │         dj │ Punto inicial   │ Punto final   │\n",
            "╞═════╪═════════╪══════╪═══════════╪═══════════╪════════════╪═════════════════╪═══════════════╡\n",
            "│   0 │ S0(x)   │  4.1 │  0.333333 │  2.24422  │ -3.77704   │ (27.7, 4.1)     │ (28, 4.3)     │\n",
            "├─────┼─────────┼──────┼───────────┼───────────┼────────────┼─────────────────┼───────────────┤\n",
            "│   1 │ S1(x)   │  4.3 │  0.660066 │ -1.15512  │  0.29505   │ (28, 4.3)       │ (29, 4.1)     │\n",
            "├─────┼─────────┼──────┼───────────┼───────────┼────────────┼─────────────────┼───────────────┤\n",
            "│   2 │ S2(x)   │  4.1 │ -0.765017 │ -0.269967 │ -0.0650165 │ (29, 4.1)       │ (30, 3.0)     │\n",
            "╘═════╧═════════╧══════╧═══════════╧═══════════╧════════════╧═════════════════╧═══════════════╛\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Se puede ver que es exactamente el mismo Spline que se obtiene al utilizar el algoritmo implementado previamente."
      ],
      "metadata": {
        "id": "SGMukkmD3l8S"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "polinomio = SplineCubico(x_curva3, a_curva3, fp0_curva3, fpn_curva3)\n",
        "polinomio.construir_spline_cubico()\n",
        "polinomio.obtener_todos_los_Sj()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 73
        },
        "outputId": "86a038e0-6b5f-4985-f4e8-5bc6b480b640",
        "id": "JyACZsBc3l8S"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'S0(x) = (4.1) + (0.333333333000000)(x-27.7) + (2.24422442422441)(x-27.7)^2 + (-3.77704437334064)(x-27.7)^3'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'S1(x) = (4.3) + (0.660066006732671)(x-28) + (-1.15511551178218)(x-28)^2 + (0.295049505049504)(x-28)^3'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'S2(x) = (4.1) + (-0.765016501683168)(x-29) + (-0.269966996633663)(x-29)^2 + (-0.0650165016831685)(x-29)^3'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### $\\quad$ **e)** $\\textrm{Reproduzca la figura 2.1 muestreando las splines encontradas en el punto anterior }$ $\\textrm{a un paso lo suficientemente pequeño para obtener una visualizacion suave de la misma.}$"
      ],
      "metadata": {
        "id": "Nb8Z8DVjEmm6"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt \n",
        "from sympy import *\n",
        "import random\n",
        "\n",
        "#vector de colores random\n",
        "color=[\"#\"+''.join([random.choice('0123456789ABCDEF') for i in range(6)]) for j in range(18)]\n",
        "\n",
        "#puntos a interpolar\n",
        "x_coord = [1,2,5,6,7,8,10,13,17,20,23,24,25,27,27.7,28,29,30]\n",
        "y_coord = [3.0,3.7,3.9,4.2,5.7,6.6,7.1,6.7,4.5,7.0,6.1,5.6,5.8,5.2,4.1,4.3,4.1,3.0]\n",
        "\n",
        "#limites de cada curva\n",
        "x = [None]*(len(x_coord)-1)\n",
        "for i in range(len(x_coord)-1):\n",
        "  x[i] = np.linspace(x_coord[i], x_coord[i+1])"
      ],
      "metadata": {
        "id": "Fj2RmIjHwAFc"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### $\\textrm{Visualizacion completa}$"
      ],
      "metadata": {
        "id": "grN-V3RaNKo7"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#tamaño\n",
        "plt.figure(figsize=(20,6))\n",
        "\n",
        "#separacion de ejes\n",
        "plt.xticks(np.arange(0, 30, 1)) \n",
        "plt.yticks(np.arange(2, 8, 0.5)) \n",
        "\n",
        "#puntos a interpolar\n",
        "plt.scatter(x_coord, y_coord, label= \"puntos\", color= \"red\", marker= \"o\", s=100) \n",
        "    \n",
        "#____________definición curvas\n",
        "\n",
        "#curva 1\n",
        "for i in range(len(x_curva1)-1):\n",
        "  plt.plot( x[i],\n",
        "           [(a_curva1[i] +\n",
        "              b_curva1[i]*(x-x_curva1[i]) +\n",
        "              c_curva1[i]*(x-x_curva1[i])**2 +\n",
        "              d_curva1[i]*(x-x_curva1[i])**3\n",
        "            ) for x in x[i]],\n",
        "           c=color[i],\n",
        "           label='''1: S{i}(x)'''.format(i=i)\n",
        "          )\n",
        "\n",
        "#curva 2\n",
        "for j in range(len(x_curva2)-1):\n",
        "  plt.plot( x[len(x_curva1)-1+j],\n",
        "          [(  a_curva2[j] +\n",
        "              b_curva2[j]*(x-x_curva2[j]) +\n",
        "              c_curva2[j]*(x-x_curva2[j])**2 +\n",
        "              d_curva2[j]*(x-x_curva2[j])**3\n",
        "            ) for x in x[len(x_curva1)-1+j]],\n",
        "           c=color[i+j+1],\n",
        "           label='''2: S{j}(x)'''.format(j=j)\n",
        "          )\n",
        "\n",
        "#curva 3\n",
        "for k in range(len(x_curva3)-1):\n",
        "  plt.plot( x[i+j+2+k],\n",
        "          [(  a_curva3[k] +\n",
        "              b_curva3[k]*(x-x_curva3[k]) +\n",
        "              c_curva3[k]*(x-x_curva3[k])**2 +\n",
        "              d_curva3[k]*(x-x_curva3[k])**3\n",
        "            ) for x in x[i+j+2+k]],\n",
        "           c=color[i+j+k+2],\n",
        "           label='''3: S{k}(x)'''.format(k=k)\n",
        "          )\n",
        "\n",
        "#labels\n",
        "plt.title(\"Gráfico de los splines cúbicos obtenidos\", fontsize=20)\n",
        "plt.xlabel(\"Eje x\", fontsize=12)\n",
        "plt.ylabel(\"Eje y\", fontsize=12)\n",
        "plt.legend(fontsize = \"large\", ncol=8, loc = \"lower center\")\n",
        "\n",
        "plt.grid()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 413
        },
        "id": "DyNOCDEJ2g_N",
        "outputId": "3f3fc0c9-6928-4ddb-82fb-afb84f4469fb"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1440x432 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### $\\textrm{Visualizacion curva 1}$"
      ],
      "metadata": {
        "id": "fS4FjckSNcRk"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt \n",
        "from sympy import *\n",
        "import random\n",
        "\n",
        "#tamaño\n",
        "plt.figure(figsize=(20,6))\n",
        "plt.xlim(0.5, 17.5)\n",
        "plt.ylim(2.5,7.5)\n",
        "\n",
        "#separacion de ejes\n",
        "plt.xticks(np.arange(0.5, 17.5, 0.5)) \n",
        "plt.yticks(np.arange(2, 8, 0.5)) \n",
        "\n",
        "#puntos a interpolar\n",
        "plt.scatter(x_coord, y_coord, label= \"puntos\", color= \"red\", marker= \"o\", s=100) \n",
        "\n",
        "#definición curvas\n",
        "\n",
        "#curva 1\n",
        "for i in range(len(x_curva1)-1):\n",
        "  plt.plot( x[i],\n",
        "           [( a_curva1[i] +\n",
        "              b_curva1[i]*(x-x_curva1[i]) +\n",
        "              c_curva1[i]*(x-x_curva1[i])**2 +\n",
        "              d_curva1[i]*(x-x_curva1[i])**3\n",
        "            ) for x in x[i]],\n",
        "           c=color[i],\n",
        "           label='''1: S{i}(x)'''.format(i=i)\n",
        "          )\n",
        "\n",
        "#curva 2: solo S0\n",
        "plt.plot(x[len(x_curva1)-1],\n",
        "         [(a_curva2[0]+b_curva2[0]*(x-x_curva2[0])+c_curva2[0]*(x-x_curva2[0])**2 +d_curva2[0]*(x-x_curva2[0])**3\n",
        "           ) for x in x[len(x_curva1)-1]],\n",
        "           c=color[i+1])\n",
        "\n",
        "#labels\n",
        "plt.title(\"Gráfico del spline cúbico 1\", fontsize=20)\n",
        "plt.xlabel(\"Eje x\", fontsize=12)\n",
        "plt.ylabel(\"Eje y\", fontsize=12)\n",
        "plt.legend(fontsize = \"large\",ncol=10, loc = \"lower center\")\n",
        "\n",
        "plt.grid()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 413
        },
        "outputId": "dbcd760a-0f8d-4409-f306-1dd457716498",
        "id": "IWZ_gSzKNcRl"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1440x432 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### $\\textrm{Visualizacion curva 2}$"
      ],
      "metadata": {
        "id": "C2hm6noTPAmm"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt \n",
        "from sympy import *\n",
        "import random\n",
        "\n",
        "#tamaño\n",
        "plt.figure(figsize=(20,6))\n",
        "plt.xlim(16.5, 28)\n",
        "plt.ylim(4,7.5)\n",
        "\n",
        "#separacion de ejes\n",
        "plt.xticks(np.arange(16.5, 28, 0.5)) \n",
        "plt.yticks(np.arange(4, 7.5, 0.5)) \n",
        "\n",
        "#puntos a interpolar\n",
        "plt.scatter(x_coord, y_coord, label= \"puntos\", color= \"red\", marker= \"o\", s=100) \n",
        "\n",
        "#definición curvas\n",
        "\n",
        "tope = len(x_curva1)-2\n",
        "#curva 1: solo último Sj\n",
        "plt.plot(x[tope],\n",
        "         [(a_curva1[tope]+b_curva1[tope]*(x-x_curva1[tope])+c_curva1[tope]*(x-x_curva1[tope])**2+d_curva1[tope]*(x-x_curva1[tope])**3) for x in x[tope]],\n",
        "           c=color[tope])\n",
        "\n",
        "i = tope\n",
        "#curva 2\n",
        "for j in range(len(x_curva2)-1):\n",
        "  plt.plot( x[len(x_curva1)-1+j],\n",
        "          [(  a_curva2[j] +\n",
        "              b_curva2[j]*(x-x_curva2[j]) +\n",
        "              c_curva2[j]*(x-x_curva2[j])**2 +\n",
        "              d_curva2[j]*(x-x_curva2[j])**3\n",
        "            ) for x in x[len(x_curva1)-1+j]],\n",
        "           c=color[i+j+1],\n",
        "           label='''2: S{j}(x)'''.format(j=j)\n",
        "           )\n",
        "\n",
        "#curva 3: solo S0\n",
        "plt.plot(x[i+j+2],\n",
        "          [(a_curva3[0]+b_curva3[0]*(x-x_curva3[0])+c_curva3[0]*(x-x_curva3[0])**2+d_curva3[0]*(x-x_curva3[0])**3) for x in x[i+j+2]],\n",
        "           c=color[i+j+2])\n",
        "\n",
        "#labels\n",
        "plt.title(\"Gráfico del spline cúbico 2\", fontsize=20)\n",
        "plt.xlabel(\"Eje x\", fontsize=12)\n",
        "plt.ylabel(\"Eje y\", fontsize=12)\n",
        "plt.legend(fontsize = \"large\",ncol=10, loc = \"lower center\")\n",
        "\n",
        "plt.grid()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 413
        },
        "outputId": "82c91f60-2fd9-49a3-e843-83c009ecf27d",
        "id": "wsKRcRRSPAmw"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1440x432 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### $\\textrm{Visualizacion curva 3}$"
      ],
      "metadata": {
        "id": "q2elwqiGR8Hn"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt \n",
        "from sympy import *\n",
        "import random\n",
        "\n",
        "#tamaño\n",
        "plt.figure(figsize=(20,6))\n",
        "plt.xlim(27.5, 30)\n",
        "plt.ylim(3,4.5)\n",
        "\n",
        "#separacion de ejes\n",
        "plt.xticks(np.arange(27.5, 30, 0.25)) \n",
        "plt.yticks(np.arange(3, 4.5, 0.25)) \n",
        "\n",
        "#puntos a interpolar\n",
        "plt.scatter(x_coord, y_coord, label= \"puntos\", color= \"red\", marker= \"o\", s=100) \n",
        "\n",
        "#definición curvas\n",
        "\n",
        "i = len(x_curva1)-2\n",
        "\n",
        "#curva 2: Solo el último Sj\n",
        "tope = len(x_curva2)-2\n",
        "plt.plot( x[len(x_curva1)-1+tope],\n",
        "          [(a_curva2[tope]+b_curva2[tope]*(x-x_curva2[tope]) +\n",
        "              c_curva2[tope]*(x-x_curva2[tope])**2 +\n",
        "              d_curva2[tope]*(x-x_curva2[tope])**3\n",
        "            ) for x in x[len(x_curva1)-1+tope]],\n",
        "           c=color[i+tope+1]\n",
        "           )\n",
        "\n",
        "#curva 3\n",
        "for k in range(len(x_curva3)-1):\n",
        "  plt.plot( x[i+j+2+k],\n",
        "          [(  a_curva3[k] +\n",
        "              b_curva3[k]*(x-x_curva3[k]) +\n",
        "              c_curva3[k]*(x-x_curva3[k])**2 +\n",
        "              d_curva3[k]*(x-x_curva3[k])**3\n",
        "            ) for x in x[i+j+2+k]],\n",
        "           c=color[i+j+k+2],\n",
        "           label='''3: S{k}(x)'''.format(k=k)\n",
        "          )\n",
        "\n",
        "#labels\n",
        "plt.title(\"Gráfico del spline cúbico 3\", fontsize=20)\n",
        "plt.xlabel(\"Eje x\", fontsize=12)\n",
        "plt.ylabel(\"Eje y\", fontsize=12)\n",
        "plt.legend(fontsize = \"large\",ncol=10, loc = \"lower center\")\n",
        "\n",
        "plt.grid()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 413
        },
        "outputId": "fc84ba5b-d7a3-4a40-d6ff-c98da746a102",
        "id": "qLYpHKKKR8Hn"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1440x432 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}