notebooks/3-calculus-i.ipynb

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    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
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      "source": [
        "<a href=\"https://colab.research.google.com/github/joanby/matematicas-ml/blob/master/3_calculus_i.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aTOLgsbN69-P"
      },
      "source": [
        "# Cálculo I: Límites & Derivadas"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yqUB9FTRAxd-"
      },
      "source": [
        "Este tema, *Cálculo I: Límites y Derivadas*, introduce el campo matemático del cálculo -el estudio de las tasas de cambio- desde cero. Es esencial porque el cálculo de derivadas a través de la diferenciación es la base de la optimización de la mayoría de los algoritmos de aprendizaje automático, incluidos los utilizados en el aprendizaje profundo, como la retropropagación y el descenso de gradiente estocástico.\n",
        "\n",
        "A través de la exposición mesurada de la teoría junto con ejemplos interactivos, desarrollarás una comprensión práctica de cómo se utiliza el cálculo para calcular límites y diferenciar funciones. También aprenderá a aplicar la diferenciación automática en las populares bibliotecas de aprendizaje automático TensorFlow 2 y PyTorch. El contenido cubierto en esta clase es en sí mismo fundamental para varios otros temas de la serie *Fundamentos del Aprendizaje Automático*, especialmente *Cálculo II* y *Optimización*."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "d4tBvI88BheF"
      },
      "source": [
        "En el transcurso del estudio de este tema, vamos a:\n",
        "\n",
        "* Desarrollar una comprensión de lo que está pasando bajo el capó de los algoritmos de aprendizaje automático, incluidos los utilizados para el aprendizaje profundo.\n",
        "* Ser capaz de comprender más íntimamente los detalles de los papeles de aprendizaje automático, así como muchos de los otros temas que subyacen ML, incluyendo el cálculo de derivadas parciales, estadísticas y algoritmos de optimización.\n",
        "* Calcular las derivadas de funciones, incluyendo el uso de AutoDiff en las populares bibliotecas TensorFlow 2 y PyTorch."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Z68nQ0ekCYhF"
      },
      "source": [
        "**Tenga en cuenta que este cuaderno Jupyter no está diseñado para funcionar por sí solo. Es el código que acompaña a una clase o a los vídeos de la serie [Fundamentos Matemáticos de Machine Learning](https://github.com/joanby/matematicas-ml) de Frogames Formación, que ofrecen detalles sobre lo siguiente:**\n",
        "\n",
        "*Segmento 1: Límites*\n",
        "\n",
        "* Qué es el cálculo\n",
        "* Breve historia del cálculo\n",
        "* El método de agotamiento\n",
        "* Cálculo de límites\n",
        "\n",
        "*Segmento 2: Cálculo de Derivadas con Diferenciación*\n",
        "* El Método Delta\n",
        "* La Ecuación de Diferenciación\n",
        "* Notación de derivadas\n",
        "* La regla de la potencia\n",
        "* Regla de los múltiplos constantes\n",
        "* Regla de la suma\n",
        "* Regla del producto\n",
        "* Regla del cociente\n",
        "* La regla de la cadena\n",
        "\n",
        "*Segmento 3: Diferenciación Automática*\n",
        "* AutoDiff con PyTorch\n",
        "* AutoDiff con TensorFlow 2\n",
        "* Aprendizaje automático mediante diferenciación\n",
        "* Funciones de Coste (o Pérdida)\n",
        "* El Futuro: Programación Diferenciable"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1SHRQmz0cxYw"
      },
      "source": [
        "## Segmento 1: Límites"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ab2YePNtcxYx"
      },
      "source": [
        "### El Cálculo de Infinitesimales"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Bzug184ZcxYx"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Kgjg4q4kcxY1"
      },
      "source": [
        "x = np.linspace(-10, 10, 10000) # inicio, final, n puntos"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MHWrqwBacxY4"
      },
      "source": [
        "Si $y = x^2 + 2x + 2$:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "y4oTgUY_cxY5"
      },
      "source": [
        "y = x**2 + 2*x + 2"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5OxJjePDcxY8",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 451
        },
        "outputId": "04100cf4-b76b-429b-c59e-f5a20646e5b8"
      },
      "source": [
        "fig, ax = plt.subplots()\n",
        "_ = ax.plot(x,y)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5IjlYM5LcxY_"
      },
      "source": [
        "* No hay líneas rectas en la curva.\n",
        "* Sin embargo, si nos acercamos _infinitamente_, observamos curvas que se _aproximan_ a rectas.\n",
        "* Esto nos permite encontrar una pendiente $m$ (tangente) en cualquier punto de la curva, incluso identificar dónde $m = 0$:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nJ1n043-cxZA",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 456
        },
        "outputId": "34c4f066-9e1a-41ee-bb48-a5cbaf561745"
      },
      "source": [
        "fig, ax = plt.subplots()\n",
        "ax.set_xlim([-2, -0])\n",
        "ax.set_ylim([0, 2])\n",
        "_ = ax.plot(x,y)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tgrXcqfScxZD",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 451
        },
        "outputId": "d993b011-5481-415d-cd91-6790758dcf37"
      },
      "source": [
        "fig, ax = plt.subplots()\n",
        "ax.set_xlim([-1.5, -0.5])\n",
        "ax.set_ylim([0.5, 1.5])\n",
        "_ = ax.plot(x,y)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8osTRq2AcxZG",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 456
        },
        "outputId": "a897d15a-c023-48c1-d761-880000b3e197"
      },
      "source": [
        "fig, ax = plt.subplots()\n",
        "ax.set_xlim([-1.1, -0.9])\n",
        "ax.set_ylim([0.9, 1.1])\n",
        "_ = ax.plot(x,y)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tpcDMwpDcxZJ",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 456
        },
        "outputId": "2cd49655-022b-4e12-9248-52702fbf0774"
      },
      "source": [
        "fig, ax = plt.subplots()\n",
        "ax.set_xlim([-1.01, -0.99])\n",
        "ax.set_ylim([0.99, 1.01])\n",
        "_ = ax.plot(x,y)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BJ0B4YNPcxZL"
      },
      "source": [
        "**Volver a las slides aquí.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "38-6wbQocxZL"
      },
      "source": [
        "### Límites"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "S7GSdz-ucxZM",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 456
        },
        "outputId": "0ece3c02-3932-461e-c2e5-5224592b930a"
      },
      "source": [
        "fig, ax = plt.subplots()\n",
        "plt.axvline(x=0, color='lightgray')\n",
        "plt.axhline(y=0, color='lightgray')\n",
        "plt.xlim(-5, 10)\n",
        "plt.ylim(-10, 80)\n",
        "plt.axvline(x=5, color='purple', linestyle='--')\n",
        "plt.axhline(y=37, color='purple', linestyle='--')\n",
        "_ = ax.plot(x,y)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AaRfRUYtcxZO"
      },
      "source": [
        "$$\\lim_{x \\to 1} \\frac{x^2 - 1}{x - 1}$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZdDhpdiPcxZO"
      },
      "source": [
        "def my_fxn(my_x):\n",
        "    my_y = (my_x**2 - 1)/(my_x - 1)\n",
        "    return my_y"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5xKbepf445LM",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "5f140a03-e0f1-4ee4-e9df-d13a08a6f8a6"
      },
      "source": [
        "my_fxn(2)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "3.0"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "umrgvf3BcxZQ"
      },
      "source": [
        "# Descomentar la siguiente línea produce un error de 'división por cero':\n",
        "# my_fxn(1)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yeGqX8oscxZS",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ca18d658-3ee3-4fa4-a984-e9405f1cfbf1"
      },
      "source": [
        "my_fxn(0.9)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1.9"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4unTKbu8cxZU",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ca2b6256-0a72-4e19-85ac-83c3438e50e6"
      },
      "source": [
        "my_fxn(0.999)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1.9989999999999712"
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YuVfXKa5cxZW",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "bdf7b66f-9799-4ec8-9e43-c80b56aa059a"
      },
      "source": [
        "my_fxn(1.1)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "2.1"
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "x4eY1qWEcxZY",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "956ad653-3731-4ab4-ea61-1f3d76f24fb0"
      },
      "source": [
        "my_fxn(1.001)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "2.0009999999999177"
            ]
          },
          "metadata": {},
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pjUtPQwAcxZb"
      },
      "source": [
        "y = my_fxn(x)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Tg4Ow8k3cxZe",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 456
        },
        "outputId": "9ea369ac-7ea7-43c6-d5c0-5ac93280133b"
      },
      "source": [
        "fig, ax = plt.subplots()\n",
        "plt.axvline(x=0, color='lightgray')\n",
        "plt.axhline(y=0, color='lightgray')\n",
        "plt.xlim(-1, 5)\n",
        "plt.ylim(-1, 5)\n",
        "plt.axvline(x=1, color='purple', linestyle='--')\n",
        "plt.axhline(y=2, color='purple', linestyle='--')\n",
        "_ = ax.plot(x,y)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VQWYjKjVcxZf"
      },
      "source": [
        "**Volver a las slides aquí.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hc3PDahDcxZg"
      },
      "source": [
        "$$\\lim_{x \\to 0} \\frac{\\text{sin } x}{x}$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XDLZLagKcxZg"
      },
      "source": [
        "def sin_fxn(my_x):\n",
        "    my_y = np.sin(my_x)/my_x\n",
        "    return my_y"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HU-B5ebBcxZi"
      },
      "source": [
        "# Descomentar la siguiente línea produce un error de 'división por cero':\n",
        "# y = sin_fxn(0)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YjIqAWnwcxZk",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "5a2aa882-aec5-45aa-abe8-01a240d7d7e9"
      },
      "source": [
        "sin_fxn(0.1)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.9983341664682815"
            ]
          },
          "metadata": {},
          "execution_count": 21
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mmTAnugUcxZm",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b577dd5b-5304-49d6-b375-afb7b64665ab"
      },
      "source": [
        "sin_fxn(0.001)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.9999998333333416"
            ]
          },
          "metadata": {},
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UFM_c1t_cxZp",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "011a6a32-1d2c-48f7-93b6-3c71cce2bb39"
      },
      "source": [
        "sin_fxn(-0.1)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.9983341664682815"
            ]
          },
          "metadata": {},
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xrSXdv0ScxZr",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "a88f5943-0f10-498c-fe2d-67238a14c5a4"
      },
      "source": [
        "sin_fxn(-0.001)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.9999998333333416"
            ]
          },
          "metadata": {},
          "execution_count": 24
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5nhhRmJTcxZs"
      },
      "source": [
        "y = sin_fxn(x)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bolWRmXmcxZu",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 456
        },
        "outputId": "91f27f15-b68c-42f6-b545-a8b74acabd5e"
      },
      "source": [
        "fig, ax = plt.subplots()\n",
        "plt.axvline(x=0, color='lightgray')\n",
        "plt.axhline(y=0, color='lightgray')\n",
        "plt.xlim(-10, 10)\n",
        "plt.ylim(-1, 2)\n",
        "plt.axvline(x=0, color='purple', linestyle='--')\n",
        "plt.axhline(y=1, color='purple', linestyle='--')\n",
        "_ = ax.plot(x,y)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2OI8JVY6cxZw"
      },
      "source": [
        "**Volver a las slides aquí.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ly5b30kjcxZx"
      },
      "source": [
        "$$ \\lim_{x \\to \\infty} \\frac{25}{x} $$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-WbP-XFncxZy"
      },
      "source": [
        "def inf_fxn(my_x):\n",
        "    my_y = 25/my_x\n",
        "    return my_y"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "C-35M67YcxZ3",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "426e7e5c-415c-4073-e7d3-6b9b2f4dd078"
      },
      "source": [
        "inf_fxn(1e3)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.025"
            ]
          },
          "metadata": {},
          "execution_count": 28
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jZ88FSTfcxZ5",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d1a6c0cb-1acd-481b-92bf-4bd9adbba65e"
      },
      "source": [
        "inf_fxn(1e6)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "2.5e-05"
            ]
          },
          "metadata": {},
          "execution_count": 29
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PwTJXJWWeDZT"
      },
      "source": [
        "y = inf_fxn(x)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AwwKi3RMeBjV",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 456
        },
        "outputId": "d160c98e-af21-4df5-bae3-c3498d1ae4f9"
      },
      "source": [
        "fig, ax = plt.subplots()\n",
        "plt.axvline(x=0, color='lightgray')\n",
        "plt.axhline(y=0, color='lightgray')\n",
        "plt.xlim(-10, 10)\n",
        "plt.ylim(-300, 300)\n",
        "_ = ax.plot(x, y)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2Rjoo4OKbmnB"
      },
      "source": [
        "left_x = x[x<0]\n",
        "right_x = x[x>0]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sb9QiH6vcxZ0"
      },
      "source": [
        "left_y = inf_fxn(left_x)\n",
        "right_y = inf_fxn(right_x)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vleskD0VcxZ7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 456
        },
        "outputId": "59fb7362-9355-4ff4-9b65-1ae5d233902e"
      },
      "source": [
        "fig, ax = plt.subplots()\n",
        "plt.axvline(x=0, color='lightgray')\n",
        "plt.axhline(y=0, color='lightgray')\n",
        "plt.xlim(-10, 10)\n",
        "plt.ylim(-300, 300)\n",
        "ax.plot(left_x, left_y, c='C0')\n",
        "_ = ax.plot(right_x, right_y, c='C0')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bA2xg33LcxZ8"
      },
      "source": [
        "**Ejercicios:**\n",
        "\n",
        "Evalúa los límites siguientes utilizando las técnicas de las diapositivas o las anteriores.\n",
        "\n",
        "1. $$ \\lim_{x \\to 0} \\frac{x^2-1}{x-1} $$\n",
        "2. $$ \\lim_{x \\to -5} \\frac{x^2-25}{x+5} $$\n",
        "3. $$ \\lim_{x \\to 4} \\frac{x^2 -2x -8}{x-4} $$\n",
        "4. $$ \\lim_{x \\to -\\infty} \\frac{25}{x} $$\n",
        "5. $$ \\lim_{x \\to 0} \\frac{25}{x} $$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zIhHIcmzLTQQ"
      },
      "source": [
        "Para tu información: Aunque no es necesario para ML ni para este currículo de *Fundamentos de ML*, la librería de matemáticas simbólicas [SymPy](https://www.sympy.org/en/index.html) incluye un método `limits()`. Puedes leer sobre su aplicación para evaluar límites de expresiones [aquí](https://www.geeksforgeeks.org/python-sympy-limit-method/)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AbAn1ChdcxZ9"
      },
      "source": [
        "**Volver a las slides aquí.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "e7cnhfOYcxZ9"
      },
      "source": [
        "## Segmento 2: Cálculo de Derivadas con Diferenciación"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CDn8BeCDcxZ9"
      },
      "source": [
        "Traigamos de vuelta a nuestro viejo amigo $y = x^2 + 2x + 2$:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Dk2EXlqccxZ-"
      },
      "source": [
        "def f(my_x):\n",
        "    my_y = my_x**2 + 2*my_x + 2\n",
        "    return my_y"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SLmyyYdEcxaA"
      },
      "source": [
        "y = f(x)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eNIlXWeQcxaC",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 451
        },
        "outputId": "5c295729-5bc2-4ce3-b8bc-c2fe7b6a5323"
      },
      "source": [
        "fig, ax = plt.subplots()\n",
        "plt.axvline(x=0, color='lightgray')\n",
        "plt.axhline(y=0, color='lightgray')\n",
        "_ = ax.plot(x,y)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "h7C7nPEhcxaD"
      },
      "source": [
        "Identifiquemos la pendiente por ejemplo en $x = 2$."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DeVa3RrtcxaE"
      },
      "source": [
        "Primero determinemos el valor de y $y$:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hz5oolNEcxaE",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d9a7574e-f33e-4837-ad27-13b9279cc910"
      },
      "source": [
        "f(2)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "10"
            ]
          },
          "metadata": {},
          "execution_count": 38
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7fkzBRR5cxaF"
      },
      "source": [
        "Guay. Llamemos a este punto $P$, que se encuentra en (2, 10):"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IOI2oxj2cxaG",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "f60d568f-c926-4a70-d5ca-2783fc50082c"
      },
      "source": [
        "fig, ax = plt.subplots()\n",
        "plt.axvline(x=0, color='lightgray')\n",
        "plt.axhline(y=0, color='lightgray')\n",
        "plt.scatter(2, 10) # new\n",
        "_ = ax.plot(x,y)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PPCiF6CacxaI"
      },
      "source": [
        "El *método delta* utiliza la diferencia entre dos puntos para calcular la pendiente. Para ilustrarlo, definamos otro punto, $Q$ donde, digamos, $x = 5$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YAP0LJnxcxaI",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "3efdf4f2-51ab-4441-c2d7-619f0972e67a"
      },
      "source": [
        "f(5)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "37"
            ]
          },
          "metadata": {},
          "execution_count": 39
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "usfMMyTvcxaK",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 451
        },
        "outputId": "68dc1212-d692-4666-f3c1-61d19f5823cd"
      },
      "source": [
        "fig, ax = plt.subplots()\n",
        "plt.axvline(x=0, color='lightgray')\n",
        "plt.axhline(y=0, color='lightgray')\n",
        "plt.scatter(2, 10)\n",
        "plt.scatter(5, 37, c = 'orange', zorder=3) # new\n",
        "_ = ax.plot(x,y)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kdony9sucxaM"
      },
      "source": [
        "Hallar la pendiente $m$ entre los puntos $P$ y $Q$:$$m = \\frac{\\text{cambio en }y}{\\text{cambio en }x} = \\frac{\\Delta y}{\\Delta x} = \\frac{y_2 - y_1}{x_2 - x_1} = \\frac{37-10}{5-2} = \\frac{27}{3} = 9$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kgoU-_wzcxaM",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ed2e9d94-e053-450b-ba71-af363abb875e"
      },
      "source": [
        "m = (37-10)/(5-2)\n",
        "m"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "9.0"
            ]
          },
          "metadata": {},
          "execution_count": 41
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZWtSUfLVcxaP"
      },
      "source": [
        "Para representar la recta que pasa por $P$ y $Q$, podemos reordenar la ecuación de la recta $y = mx + b$ para resolver $b$:\n",
        "$$b = y - mx$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UuYXrltscxaP",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e0bb2cf2-e457-4d95-829f-4ea721dd3c73"
      },
      "source": [
        "b = 37-m*5\n",
        "b"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "-8.0"
            ]
          },
          "metadata": {},
          "execution_count": 42
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AwawB1LLcxaR"
      },
      "source": [
        "line_y = m*x + b"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Lkg2Bl7TcxaT",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 451
        },
        "outputId": "f9eb48b2-12df-46f4-aa6f-3793d4b7d2f8"
      },
      "source": [
        "fig, ax = plt.subplots()\n",
        "plt.axvline(x=0, color='lightgray')\n",
        "plt.axhline(y=0, color='lightgray')\n",
        "plt.scatter(2, 10)\n",
        "plt.scatter(5, 37, c='orange', zorder=3)\n",
        "plt.ylim(-5, 150) # new\n",
        "plt.plot(x, line_y, c='orange') # new\n",
        "_ = ax.plot(x,y)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RGEaUT_OcxaV"
      },
      "source": [
        "Cuanto más se acerque $Q$ a $P$, más se acercará la pendiente $m$ a ser la verdadera tangente del punto $P$. Vamos a demostrarlo con otro punto $Q$ en $x = 2,1$."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xWAJUiEbcxaV"
      },
      "source": [
        "Antes, nuestra $\\Delta x$ entre $Q$ y $P$ era igual a 3. Ahora es mucho menor: $$\\Delta x = x_2 - x_1 = 2,1 - 2 = 0,1 $$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-XDEG_o7cxaV",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "cfe7c48e-8360-407a-f5f8-0194cefe8052"
      },
      "source": [
        "f(2.1)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "10.61"
            ]
          },
          "metadata": {},
          "execution_count": 46
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "85n3ApTmcxaX",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 451
        },
        "outputId": "574a9bd4-1e82-44cc-8e62-ad81bf4507ff"
      },
      "source": [
        "fig, ax = plt.subplots()\n",
        "plt.axvline(x=0, color='lightgray')\n",
        "plt.axhline(y=0, color='lightgray')\n",
        "plt.scatter(2, 10)\n",
        "plt.scatter(2.1, 10.61, c = 'orange', zorder=3)\n",
        "_ = ax.plot(x,y)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YlWhoumBcxaY",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0a1644db-fb29-46b1-ce88-c5682bec8652"
      },
      "source": [
        "m = (10.61-10)/(2.1-2)\n",
        "m"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "6.099999999999989"
            ]
          },
          "metadata": {},
          "execution_count": 48
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KHMZNdjQcxaa",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "451a2688-fe51-43a0-b72b-130df516b85a"
      },
      "source": [
        "b = 10.61-m*2.1\n",
        "b"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "-2.199999999999978"
            ]
          },
          "metadata": {},
          "execution_count": 49
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "J1-_0DBJcxab"
      },
      "source": [
        "line_y = m*x + b"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eDtjdRYQcxad",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 451
        },
        "outputId": "98df9156-3cb0-4238-f191-7fe3d6682fcb"
      },
      "source": [
        "fig, ax = plt.subplots()\n",
        "plt.axvline(x=0, color='lightgray')\n",
        "plt.axhline(y=0, color='lightgray')\n",
        "plt.scatter(2, 10)\n",
        "plt.scatter(2.1, 10.61, c='orange', zorder=3)\n",
        "plt.ylim(-5, 150)\n",
        "plt.plot(x, line_y, c='orange', zorder=3)\n",
        "_ = ax.plot(x,y)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "elxPRnoTcxae"
      },
      "source": [
        "Cuanto más se acerca $Q$ a $P$ (es decir, $\\Delta x$ se aproxima a 0), más claro resulta que la pendiente $m$ en el punto $P$ = (2, 10) es igual a 6."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "srMjU62xcxaf"
      },
      "source": [
        "Hagamos $\\Delta x$ extremadamente pequeño, 0,000001, para ilustrar esto:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "c_B0wY47cxaf",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7c538275-5c2a-4f78-ea62-256c2c794309"
      },
      "source": [
        "delta_x = 0.000001\n",
        "delta_x"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1e-06"
            ]
          },
          "metadata": {},
          "execution_count": 52
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "g8LSgemacxai"
      },
      "source": [
        "x1 = 2\n",
        "y1 = 10"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gsa2I2Jxcxaj"
      },
      "source": [
        "Reordenando $\\Delta x = x_2 - x_1$, podemos calcular $x_2$ para nuestro punto $Q$, que ahora está extremadamente cerca de $P$:\n",
        "$$x_2 = x_1 + \\Delta x$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4PgqVCZVcxak",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0f20e522-6d09-4ffd-8ae4-ecbb5362a605"
      },
      "source": [
        "x2 = x1 + delta_x\n",
        "x2"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "2.000001"
            ]
          },
          "metadata": {},
          "execution_count": 54
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FoBqhu1zcxan"
      },
      "source": [
        "$y_2$ para nuestro punto $Q$ se puede obtener con la función habitual $f(x)$:\n",
        "$$y_2 = f(x_2)$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9_2mjm1Ycxan",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ed78bc20-5dc6-44ea-ae93-c85dbd26fba8"
      },
      "source": [
        "y2 = f(x2)\n",
        "y2"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "10.000006000001001"
            ]
          },
          "metadata": {},
          "execution_count": 55
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Eekls7AIcxap"
      },
      "source": [
        "Para hallar la pendiente $m$, seguimos usando $$m = \\frac{\\Delta y}{\\Delta x} = \\frac{y_2 - y_1}{x_2 - x_1}$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yQAwKXPUcxap",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "fe709d02-a96b-4b79-81aa-1b863ba051b8"
      },
      "source": [
        "m = (y2 - y1)/(x2 - x1)\n",
        "m"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "6.000001000088901"
            ]
          },
          "metadata": {},
          "execution_count": 56
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IEy7jMVpcxar"
      },
      "source": [
        "¡Boom! Utilizando el método delta, hemos demostrado que en el punto $P$, la pendiente de la curva es 6."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GJ7bRkBvcxar"
      },
      "source": [
        "**Ejercicio**: Utilizando el método delta, halla la pendiente de la tangente donde $x = -1$."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pV8Vpgvdcxar"
      },
      "source": [
        "**Alerta de spoiler. La solución está abajo.**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "65FeJSRocxaz"
      },
      "source": [
        "x1 = -1"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fAIGLk8Mcxa0",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "cce60c16-1138-430b-9029-338a34503b64"
      },
      "source": [
        "y1 = f(x1)\n",
        "y1"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1"
            ]
          },
          "metadata": {},
          "execution_count": 58
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SZowMdIQcxa1"
      },
      "source": [
        "El punto $P$ está situado en (-1, 1)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-CPHl783cxa1",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "86e31469-4848-44f6-882e-b91d07fd633b"
      },
      "source": [
        "delta_x"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1e-06"
            ]
          },
          "metadata": {},
          "execution_count": 59
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jzw0J1n9cxa2",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d72c173d-2516-41b9-eabf-2902745f2b96"
      },
      "source": [
        "x2 = x1 + delta_x\n",
        "x2"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "-0.999999"
            ]
          },
          "metadata": {},
          "execution_count": 60
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WaynVKiwcxa3",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "41927312-e868-4d9a-bf2a-43439cae452a"
      },
      "source": [
        "y2 = f(x2)\n",
        "y2"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1.000000000001"
            ]
          },
          "metadata": {},
          "execution_count": 61
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rApig2ipcxa4"
      },
      "source": [
        "Un pequeño inciso: Pertinente a la definición de la diferenciación como una ecuación, una forma alternativa de calcular $y_2$ es $f(x + \\Delta x)$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yCW283sZcxa4",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "94cdd630-94dc-415b-9580-2e090c2a51ae"
      },
      "source": [
        "y2 = f(x1 + delta_x)\n",
        "y2"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1.000000000001"
            ]
          },
          "metadata": {},
          "execution_count": 62
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "S1Dr3Ankcxa7"
      },
      "source": [
        "El punto $Q$ está en (-0,999999, 1,000000000001), extremadamente cerca de $P$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZtokXlMncxa7",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "2492bf55-b2e4-44ec-9271-eb1be7601d01"
      },
      "source": [
        "m = (y2-y1)/(x2-x1)\n",
        "m"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1.0000889005535828e-06"
            ]
          },
          "metadata": {},
          "execution_count": 63
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "91slg8F4cxa8"
      },
      "source": [
        "Por tanto, como $x_2$ se acerca infinitamente a $x_1$, queda claro que la pendiente $m$ en $x_1 = -1$ es igual a cero. Vamos a trazarlo:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2WToJBOhcxa8",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8440f28f-ce0c-47ac-a3e9-b9a646fe2eb8"
      },
      "source": [
        "b = y2-m*x2\n",
        "b"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1.0000010000889006"
            ]
          },
          "metadata": {},
          "execution_count": 64
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ah0cXRhrcxa9"
      },
      "source": [
        "line_y = m*x + b"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MjLttDg9cxa-",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 451
        },
        "outputId": "c25ad899-7250-4ec0-98f5-6eeb21ed8974"
      },
      "source": [
        "fig, ax = plt.subplots()\n",
        "plt.axvline(x=0, color='lightgray')\n",
        "plt.axhline(y=0, color='lightgray')\n",
        "plt.scatter(x1, y1)\n",
        "plt.scatter(x2, y2, c='orange', zorder=3)\n",
        "plt.ylim(-5, 150)\n",
        "plt.plot(x, line_y, c='orange', zorder=3)\n",
        "_ = ax.plot(x,y)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hqmMtmpGcxbA"
      },
      "source": [
        "Como $Q$ se hace infinitamente cerca de $P$:\n",
        "* $x_2$ - $x_1$ se aproxima a 0\n",
        "* En otras palabras, $\\Delta x$ se aproxima a 0.\n",
        "* Esto se puede denotar como $\\Delta x \\to 0$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nsh_7o7kcxbA"
      },
      "source": [
        "Utilizando el método delta, hemos obtenido la definición de diferenciación a partir de los primeros principios. La derivada de $y$ (denotado $dy$) con respecto a $x$ (denotado $dx$) se puede representar como:\n",
        "$$\\frac{dy}{dx} = \\lim_{\\Delta x \\to 0} \\frac{\\Delta y}{\\Delta x}$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UxuWTEKlcxbA"
      },
      "source": [
        "Expandiendo $\\Delta y$ a $y_2 - y_1$:\n",
        "$$\\frac{dy}{dx} = \\lim_{\\Delta x \\to 0} \\frac{y_2 - y_1}{\\Delta x}$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "b0H4kFkYcxbB"
      },
      "source": [
        "Finalmente, sustituyendo $y_1$ por $f(x)$ y sustituyendo $y_2$ por $f(x + \\Delta x)$, obtenemos una representación común de la diferenciación:\n",
        "$$\\frac{dy}{dx} = \\lim_{\\Delta x \\to 0} \\frac{f(x + \\Delta x) - f(x)}{\\Delta x}$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SuYWQ9e1cxbB"
      },
      "source": [
        "Observemos la ecuación de diferenciación en acción:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Do6EHZfHcxbB"
      },
      "source": [
        "def diff_demo(my_f, my_x, my_delta):\n",
        "    return (my_f(my_x + my_delta) - my_f(my_x)) / my_delta"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hXbAgWvrcxbC"
      },
      "source": [
        "deltas = [1, 0.1, 0.01, 0.001, 0.0001, 0.00001, 0.000001]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iYtlA3S5cxbD",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "235718ab-5337-4b1c-9ac9-858a406eafbc"
      },
      "source": [
        "for delta in deltas:\n",
        "    print(diff_demo(f, 2, delta))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "7.0\n",
            "6.099999999999994\n",
            "6.009999999999849\n",
            "6.000999999999479\n",
            "6.000100000012054\n",
            "6.000009999951316\n",
            "6.000001000927568\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CMW45DQmcxbF",
        "scrolled": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "2b78dd86-bf79-4d02-f37f-88b0d3c58049"
      },
      "source": [
        "for delta in deltas:\n",
        "    print(diff_demo(f, -1, delta))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1.0\n",
            "0.10000000000000009\n",
            "0.009999999999998899\n",
            "0.001000000000139778\n",
            "9.99999993922529e-05\n",
            "1.000000082740371e-05\n",
            "1.000088900582341e-06\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Kh8vawMMcxbG"
      },
      "source": [
        "**Vuelve a las diapositivas aquí.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ez8pKj_lcxbG"
      },
      "source": [
        "## Segmento 3: Diferenciación Automatica"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "laWM6cgvcxbG"
      },
      "source": [
        "**TensorFlow** y **PyTorch** son las dos bibliotecas de diferenciación automática más populares."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RLi7jwLEzaDB"
      },
      "source": [
        "Vamos a usarlas para derivar $dy/dx$ en $x = 5$ donde:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qmgeCDWycxbL"
      },
      "source": [
        "$$y = x^2$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MhMxT9oQcxbL"
      },
      "source": [
        "$$ \\frac{dy}{dx} = 2x = 2(5) = 10 $$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Zg-PepdncxbN"
      },
      "source": [
        "### Autodiff con PyTorch"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "n8FJ1OkWcxbN"
      },
      "source": [
        "import torch"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DTYVufujcxbP"
      },
      "source": [
        "x = torch.tensor(5.0)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "13j9vFZgcxbP",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f4bf253a-96f4-4ebc-a7d7-416961f827ea"
      },
      "source": [
        "x"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(5.)"
            ]
          },
          "metadata": {},
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PBLvpsCWcxbQ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "47b6a84c-daf2-4418-c6d2-9d3f8c35dba1"
      },
      "source": [
        "x.requires_grad_() # rastrear gradientes de forma contagiosa mediante el paso hacia delante"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(5., requires_grad=True)"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zper8WoVcxbR"
      },
      "source": [
        "y = x**2"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1Pbdg7zVcxbS"
      },
      "source": [
        "y.backward() # usando autodiff"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UbV3BecacxbT",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "4501e635-b6a6-44c7-e90b-041017b03316"
      },
      "source": [
        "x.grad"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(10.)"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dyB3FghkcxbG"
      },
      "source": [
        "### Autodiff con TensorFlow"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4D12um9kcxbH"
      },
      "source": [
        "import tensorflow as tf"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "f7mQuelZcxbJ"
      },
      "source": [
        "x = tf.Variable(5.0)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "M-WeFuBfcxbK"
      },
      "source": [
        "with tf.GradientTape() as t:\n",
        "    t.watch(x) # trackeamos el forward pass\n",
        "    y = x**2"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Txjp5NBNcxbL",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d3156b6f-0d01-41d0-aae6-1c3b431be9f4"
      },
      "source": [
        "t.gradient(y, x) # usamos autodiff"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tf.Tensor: shape=(), dtype=float32, numpy=10.0>"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dS--vwVWzaDD"
      },
      "source": [
        "**Volver a las slides aquí.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "l599s7vacxbV"
      },
      "source": [
        "Como de costumbre, PyTorch se siente más intuitivo y pitónico que TensorFlow. Ver el cuaderno independiente [*Regresión en PyTorch*](https://github.com/joanby/matematicas-ml/blob/master/notebooks/regression-in-pytorch.ipynb) para un ejemplo de autodiff emparejado con descenso de gradiente para ajustar una línea de regresión simple."
      ]
    }
  ]
}