chapter02_mathematical_building_blocks_network_from_scratch.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/ayrna/deep-learning-with-python-notebooks/blob/master/chapter02_mathematical_building_blocks_network_from_scratch.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Los bloques de construcción matemáticos del aprendizaje profundo (parte I)"
      ],
      "metadata": {
        "id": "hyssLXhLvCMN"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "En este cuaderno vamos a ver: \n",
        "\n",
        "* Un ejemplo de red neuronal\n",
        "* El concepto de tensor y operaciones con tensores\n",
        "* Cómo las redes neuronales aprenden a través del algoritmo de retropropagación y el descenso por gradiente\n",
        "\n"
      ],
      "metadata": {
        "id": "hy9PB5nqwbNu"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5Nhg7HunugVa"
      },
      "source": [
        "Este cuaderno está basado en los cuadernos del libro [Deep Learning with Python, Second Edition](https://www.manning.com/books/deep-learning-with-python-second-edition?a_aid=keras&a_bid=76564dff).\n",
        "\n",
        "> This is a companion notebook for the book [Deep Learning with Python, Second Edition](https://www.manning.com/books/deep-learning-with-python-second-edition?a_aid=keras&a_bid=76564dff). For readability, it only contains runnable code blocks and section titles, and omits everything else in the book: text paragraphs, figures, and pseudocode.\n",
        "\n",
        "\n",
        "> **If you want to be able to follow what's going on, I recommend reading the notebook side by side with your copy of the book.**\n",
        "\n",
        "> This notebook was generated for TensorFlow 2.6."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wXgbqzxjugVe"
      },
      "source": [
        "# Los bloques de construcción matemáticos de las redes neuronales\n",
        "\n",
        "Vamos a hacer el típico ejemplo de clasificación de dígitos implementando una red neuronal básica en Keras. Para ello utilizaremos la famosa base de datos MNIST que contiene imágenes en escala de gris de dígitos escritos a mano (28x28 píxeles) que se agrupan en 10 categorías. \n",
        "\n",
        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)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dRhmpgLvugVf"
      },
      "source": [
        "## Un primer vistazo a una red neuronal"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Lji7ta8bugVg"
      },
      "source": [
        "**Cargando la base de datos MNIST en Keras**\n",
        "\n",
        "El conjunto de datos MNIST viene precargado en Keras como un `NumPy array`"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "mU8ATab9ugVh"
      },
      "outputs": [],
      "source": [
        "from tensorflow.keras.datasets import mnist\n",
        "(train_images, train_labels), (test_images, test_labels) = mnist.load_data()"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Veamos las características de los datos de entrenamiento:"
      ],
      "metadata": {
        "id": "bpAvOi6Sz9RH"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "yBOIF6VkugVi",
        "outputId": "9acf2402-ff2b-461a-b892-d77c1d314567"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(60000, 28, 28)"
            ]
          },
          "metadata": {},
          "execution_count": 2
        }
      ],
      "source": [
        "train_images.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "I19Hvi2EugVj",
        "outputId": "fd588609-3fe1-4d4d-b95e-07babb4f42cd"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "60000"
            ]
          },
          "metadata": {},
          "execution_count": 3
        }
      ],
      "source": [
        "len(train_labels)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "CHpMm6SNugVk",
        "outputId": "06454de3-f099-4e22-be86-a800dc7a2319"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([5, 0, 4, ..., 5, 6, 8], dtype=uint8)"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ],
      "source": [
        "train_labels"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Y los datos de test:"
      ],
      "metadata": {
        "id": "rZ0TPktx0H7L"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "RfQqRQPSugVl",
        "outputId": "a0a1318d-201b-48f1-a819-c65c2dd25e8e"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(10000, 28, 28)"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ],
      "source": [
        "test_images.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fqSJ7bclugVm",
        "outputId": "c852b9ae-d0a4-4d6f-9add-f7799d64f05b"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "10000"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ],
      "source": [
        "len(test_labels)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "47hXnHlVugVm",
        "outputId": "34dc9cfa-6082-4c3e-c2bc-fcdb1cb857fa"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([7, 2, 1, ..., 4, 5, 6], dtype=uint8)"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ],
      "source": [
        "test_labels"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wc1F0HMgugVn"
      },
      "source": [
        "**Arquitectura de la red**\n",
        "\n",
        "El bloque principal para definir una red neuronal es la `capa` (`layer`). Podemos ver las capas como una forma de filtrado de datos donde estos se van transformando progresivamente. Cada capa extrae *representaciones* de los datos que se espera que sean significativas para el problema.\n",
        "\n",
        "En este caso tenemos una secuencia de dos capas `densas` (`Dense`), que significa que están conectadas completamente (*densamente*). \n",
        "\n",
        "La última capa, es una capa de *clasificación softmax* con 10 salidas de probabilidades de pertenencia a cada clase (entre las 10 suman 1)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "-rKkVdMIugVo"
      },
      "outputs": [],
      "source": [
        "from tensorflow import keras\n",
        "from tensorflow.keras import layers\n",
        "model = keras.Sequential([\n",
        "    layers.Dense(512, activation=\"relu\"),\n",
        "    layers.Dense(10, activation=\"softmax\")\n",
        "])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VVu00wa1ugVp"
      },
      "source": [
        "**La compilacion del modelo**\n",
        "\n",
        "Para que podamos entrenar el modelo este debe *compilarse*, y para ello debemos elegir: \n",
        "* **optimizador**\n",
        "* **función de pérdida** (*loss function*)\n",
        "* **métricas de rendimiento**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "MeQE-XlfugVq"
      },
      "outputs": [],
      "source": [
        "model.compile(optimizer=\"rmsprop\",\n",
        "              loss=\"sparse_categorical_crossentropy\",\n",
        "              metrics=[\"accuracy\"])\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-EZeqKt1ugVr"
      },
      "source": [
        "**Preparación de los datos de imágenes**\n",
        "\n",
        "Necesitamos transformar nuestra matriz de datos `(60000, 28, 28)` del tipo `uint8` en el intervalor `[0, 255]` a valores reales `float32` en `[0,1]` con una matriz de dimensiones `(60000, 28 * 28)`. Nuestra red de ejemplo necesita que los datos de los patrones estén en un vector por patrón. \n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "LgPmTqC3ugVr"
      },
      "outputs": [],
      "source": [
        "train_images = train_images.reshape((60000, 28 * 28))\n",
        "train_images = train_images.astype(\"float32\") / 255\n",
        "test_images = test_images.reshape((10000, 28 * 28))\n",
        "test_images = test_images.astype(\"float32\") / 255"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Nuevo formato de las mastrices: "
      ],
      "metadata": {
        "id": "kCyMBvGo8YAk"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "train_images.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ztQNf6998bk2",
        "outputId": "4527fd77-2e5c-4c04-c7de-88ab73268f97"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(60000, 784)"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "test_images.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "FhfjYn7z8har",
        "outputId": "facc6143-ccdf-4d22-c85f-b23aa70449c7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(10000, 784)"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aJfBUtOJugVs"
      },
      "source": [
        "**\"Ajustando\" el modelo**\n",
        "\n",
        "Ya estamos listo para entrenar el modelo, que en Keras, como en muchos otros *framworks* se hace con el método `fit()`: *ajustamos* el modelo a los datos de entrenamiento.\n",
        "\n",
        "Nota: El siguiente código tardará en ejecutarse unos segundos/minutos:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Sd5HpGjvugVs",
        "outputId": "381dd9c8-1055-48fe-921c-68eeacdcc5a5"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/5\n",
            "469/469 [==============================] - 8s 15ms/step - loss: 0.2556 - accuracy: 0.9261\n",
            "Epoch 2/5\n",
            "469/469 [==============================] - 8s 16ms/step - loss: 0.1025 - accuracy: 0.9698\n",
            "Epoch 3/5\n",
            "469/469 [==============================] - 8s 17ms/step - loss: 0.0682 - accuracy: 0.9795\n",
            "Epoch 4/5\n",
            "469/469 [==============================] - 8s 17ms/step - loss: 0.0491 - accuracy: 0.9856\n",
            "Epoch 5/5\n",
            "469/469 [==============================] - 7s 15ms/step - loss: 0.0374 - accuracy: 0.9886\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<keras.callbacks.History at 0x7efff8ba1c50>"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ],
      "source": [
        "model.fit(train_images, train_labels, epochs=5, batch_size=128)"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "❓❓ \n",
        "¿Sabrías interpretar las cantidades que se van imprimiendo?\n",
        "❓❓\n",
        "\n",
        "❓❓ Prueba a cambiar el número de unidades en la capa oculta. ¿Qué sucede? ❓❓"
      ],
      "metadata": {
        "id": "1EfM6fcWMnVE"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Visualizar el modelo**"
      ],
      "metadata": {
        "id": "YHHAioEPNdPP"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from keras.utils.vis_utils import plot_model\n",
        "plot_model(model, show_shapes=True, show_layer_names=True)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 312
        },
        "id": "6q88aBNWNKKR",
        "outputId": "8fc137bd-9938-463f-a024-df1cfaabf01f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<IPython.core.display.Image object>"
            ],
            "image/png": 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1+PHj8eOPP2Lv3r1Yt24dAOC1117D7du3ATy/3LxmzRokJSVh8ODBcHV1RWRkJKqqqgA8v7xVXl6OI0eOaDzWzz77DHPnzlW5dNieSCRCVlYWQkJC8Pvf/x729vYYM2YM7t69i5ycHEyfPl1jH125ePEi3NzcMH78+B7vwxB4/P+tX4y/DmvjsT6G14bVXU/XBnVzc1Pbfvv2bRKLxXTgwAF9hWdULS0tNH36dNq/f7/QoXTp0aNHJJFIaPv27WrvrV692mhrw/L4C8OI489rwzKmD/X19fjmm29w+/Zt5QMHPj4+iI+PR3x8PGpqagSOUDctLS3Izc1FdXW1SZeti4uLw4QJExAREQHg+So3paWlOHv2LO7cuWO0OHj8hWHM8dd7svz+++/x4osvwszMDCKRCM7OzkhISNB3N73SsUyOi4tLp2V1GNPW48ePlQtpf/DBB8rtMTExWLhwIUJCQvrUYtn5+fnIyclBXl6e1nMFjW3Hjh24cuUKTpw4AQsLCwDAkSNHlAtpf/3110aLhcff+Iw+/jp8DdXJq6++SgBUyqeYGm9vb7K1tRU6DIPhy7C6M9RtiG+++Yaio6P1vt+BKjc3l7Zu3UrNzc163S+Pf98gwPgPjMuw9fX18Pf3FzqMAckY574vjO8rr7yCbdu2CR1Gv/Hmm28iJiZG7alRU8Xjr19CjP+ASJb79+9XW+2eGYcxzj2PL2PM0IyWLLUtHZOamgqJRAInJyeEh4fD1dUVEokE/v7+KusfRkREwNLSEi4uLsptK1euhI2NDUQiER49egQAiIyMxLp161BUVASRSAQfH58exf9f//VfGDNmDGxtbSGRSDBu3Dh88803AIBly5Yp7396e3srJxQvXboUUqkUtra2OHr0KIDuy+J89tlnkEqlkMlkKC8vx7p16+Dm5tbpihiGQlqUAerNuTfW+J48eRJyuRyJiYkGPV+MsQFCh2u2OunsnmVsbCwBoFOnTtHTp0+pvLycpk+fTjY2NtTY2KhsFxYWRjY2NlRYWEgNDQ1UUFBAkydPJplMRnfv3lW2W7x4MTk7O6v0m5ycTACooqJCuS0oKIi8vb3VYtTlnmVWVhbFxcXR48ePqbKykvz8/FQeSw4KCiJzc3N68OCByufeeecdOnr0qPLfH330EVlZWVF2djZVVVXRhg0byMzMjC5evKhyjlavXk27du2iBQsW0P/93/9pFWNHPblnuXnzZrK0tKQDBw7QkydP6Nq1azRx4kRydHSksrIyZbvenHtjjO/x48dJJpNRfHy8TsfPU6cGNh7/gc3k7ll2VzqmjVgsVn67GTNmDNLS0lBdXd3r8jE9FRwcjD/96U+wt7eHg4MD5s6di8rKSuVSTCtWrEBLS4tKfAqFAhcvXsQbb7wBQLeyONu2bcMf//hH5OTkYPTo0UY5xp6UAeopQ4/v7NmzoVAosGnTJr3sjzE2sAl+z7Jj6ZiuTJo0CVKptFflY/Sp7VHltoWSf/Ob3+CFF17AX//6V2XF7kOHDiEkJER5E9pQZXH0pbdlgHrD1MaXMcbaEzxZ6sLKykr5Tc7Yvv76a8yYMQNDhgyBlZUVPv74Y5X3RSIRwsPD8eOPP+LUqVMAgP/8z/9UWfOwfVmc9jUUS0pKUFdXZ7yD6YK+ywDpSsjxZYyx7vSZZNnU1NSjUjQ99d133ynXWLx79y7mz58PFxcXXLhwAU+fPlWrNwcAS5YsgUQiwb59+3Dz5k3I5XIMHz5c+X77sjjUYWX98+fPG+W4uqPvMkC6MPb4MsaYLrqsZ2lq8vPzQUTw8/NTbhOLxRov3/bU//7v/yoXJ75+/Tqamprw4YcfwsvLC8Dzb5Id2dvbY9GiRTh06BBkMhmWL1+u8r4hyuLoky5lgPR97o09vowxpguT/WbZ2tqKqqoqNDc349q1a4iMjISHhweWLFmibOPj44PHjx8jNzcXTU1NqKioQElJidq+HBwcUFpaiuLiYlRXV3f7C7ipqQkPHz5UWcm/bSX9b7/9Fg0NDbh9+3aX9+9WrFiBZ8+e4fjx45gzZ47Ke9qUxRGSLmWAenvuDT2+eXl5PHWEMaY/Ojw6q5Xvv/+efH19yczMjACQi4sLJSYm0u7du0kqlRIAGjlyJBUVFdGePXtILpcTABo+fDjdunWLiJ5PLbCwsCA3NzcSi8Ukl8tp3rx5VFRUpNJXZWUlzZw5kyQSCXl6etKqVasoKiqKAJCPj49yGsKlS5do+PDhZG1tTQEBAfQf//Ef5O3tTQC6fR0+fFjZV3R0NDk4OJCdnR0tXLiQPv/8cwJA3t7eKtMdiIh+8YtfUExMTKfn59mzZxQdHU0eHh4kFotpyJAhFBQURAUFBZSUlETW1tYEgIYNG9bragU9mTrS2tpKycnJNHLkSLKwsCB7e3uaP38+3bx5U6VdT899WVmZwce3rKyMTpw4QTKZjBISEnQ6fp46MLDx+A9s3U0dMckSXWFhYeTg4CBoDL3xxhtv0I8//ih0GCa7Nqwpj68p/Pwz4fD4D2wmN89SG21TMvqC9pd1r127BolEAk9PTwEjMn19aXwZY6zPPOBjyqKjo7FixQoQEZYuXYoDBw4IHRJjjDE9Mrlvlhs2bEB6ejqePn0KT09PZGdnCx2SRlKpFKNHj8bLL7+MuLg4jBkzRuiQTFZfHF/GGDO5ZLl161Y8e/YMRISffvoJwcHBQoekUUJCAlpaWnD37l21J2CZqr44vowxZnLJkjHGGDM1nCwZY4wxDThZMsYYYxpwsmSMMcY06HLqSGZmpjHjYAZw//59ADyWumhb0J7P2cDE4z+wdVfQQkT0/4sv/n+ZmZlYtGiRwYNijDHGTFGHtAgAWWrJkjEmnLY/Vvm/JWMmJYvvWTLGGGMacLJkjDHGNOBkyRhjjGnAyZIxxhjTgJMlY4wxpgEnS8YYY0wDTpaMMcaYBpwsGWOMMQ04WTLGGGMacLJkjDHGNOBkyRhjjGnAyZIxxhjTgJMlY4wxpgEnS8YYY0wDTpaMMcaYBpwsGWOMMQ04WTLGGGMacLJkjDHGNOBkyRhjjGnAyZIxxhjTgJMlY4wxpgEnS8YYY0wDTpaMMcaYBpwsGWOMMQ04WTLGGGMacLJkjDHGNOBkyRhjjGnAyZIxxhjTgJMlY4wxpgEnS8YYY0wDTpaMMcaYBpwsGWOMMQ04WTLGGGMaiIUOgLGB6v79+3j//ffR0tKi3FZVVQWZTIYZM2aotB01ahT+8pe/GDlCxlgbTpaMCcTd3R0lJSUoKipSe+/MmTMq//71r39trLAYY53gy7CMCei9996DhYWFxnYhISFGiIYx1hVOlowJaPHixWhubu62ja+vL8aMGWOkiBhjneFkyZiAvL29MX78eIhEok7ft7CwwPvvv2/kqBhjHXGyZExg7733HszNzTt9r7m5GQsXLjRyRIyxjjhZMiawt99+G62trWrbzczM4OfnhxEjRhg/KMaYCk6WjAnM1dUV06ZNg5mZ6n9HMzMzvPfeewJFxRhrj5MlYybg3XffVdtGRFiwYIEA0TDGOuJkyZgJCA4OVrlvaW5ujpdffhlOTk4CRsUYa8PJkjETYG9vj9/+9rfKhElECA0NFTgqxlgbTpaMmYjQ0FDlgz4WFhaYN2+ewBExxtpwsmTMRMydOxdWVlYAgDlz5mDQoEECR8QYa8PJkjETYWNjo/w2yZdgGTMtIiIioYPoysKFC5GdnS10GIwxxgwsIyMDb731ltBhdCXL5KuO+Pn5Yc2aNUKHYTLOnz+PnTt3IiMjQ+hQ+pRFixYhMjISU6dOFTqUbrW0tCAjIwPvvPOO0KGYtL4ynkw7ixYtEjoEjUz+myUAZGVlCRyJ6cjMzMSiRYtgwsNmkkQikan/5arU0NAAiUQidBgmrS+NJ9OsD4xnFt+zZMzEcKJkzPRwsmSMMcY04GTJGGOMacDJkjHGGNOAkyVjjDGmwYBJlsuWLYNMJoNIJMKVK1eEDkdwJ06cgK2tLY4dOyZ0KIwxZvIGTLLct28f9u7dK3QYJoOnnjDGmPZMflECZhizZ8/G06dPhQ4DAFBfX49Zs2bh3LlzQofCGGOdGjDfLIHnE1+Z6dm/fz/Ky8uFDoMxxrrUb5MlESE5ORmjRo2ClZUVbG1tERUVpdaupaUFmzdvhoeHB6ytrTF+/HjlUnJpaWmwsbGBVCrFkSNH8Prrr0Mul8Pd3R0HDx5U2c+ZM2cwZcoUSKVSyOVyjBs3DgqFQmMfQjh79iw8PDwgEonw+eefA9D+WFNTUyGRSODk5ITw8HC4urpCIpHA398fFy5cULaLiIiApaUlXFxclNtWrlwJGxsbiEQiPHr0CAAQGRmJdevWoaioCCKRCD4+PgCAkydPQi6XIzEx0RinhDHGukcmLDg4mIKDg3v02djYWBKJRPTnP/+ZqqqqqK6ujnbv3k0A6PLly8p2H330EVlZWVF2djZVVVXRhg0byMzMjC5evKjcDwA6deoUPX36lMrLy2n69OlkY2NDjY2NRERUU1NDcrmckpKSqL6+nsrKymjBggVUUVGhVR+6yMjIIH0M27179wgA7dq1S7lNm2MlIgoLCyMbGxsqLCykhoYGKigooMmTJ5NMJqO7d+8q2y1evJicnZ1V+k1OTiYAynNDRBQUFETe3t4q7Y4fP04ymYzi4+N7faxERAAoIyNDL/tiwuPx7F/6wHhm9stvlvX19UhJScHLL7+MtWvXws7ODtbW1nBwcFBp19DQgLS0NMyfPx9BQUGws7PDxo0bYWFhgfT0dJW2/v7+kMvlGDJkCEJCQlBbW4u7d+8CAIqLi6FQKODr6wuJRAJnZ2fk5OTA0dFRpz5MRXfH2kYsFuPFF1+ElZUVxowZg7S0NFRXV+vtmGbPng2FQoFNmzbpZX+MMdYb/TJZ3rlzB3V1dZg1a1a37W7evIm6ujqMHTtWuc3a2houLi64ceNGl5+ztLQEADQ1NQEAvLy84OTkhNDQUMTFxaG4uLjXfZiKjsfalUmTJkEqlfaJY2KMMV31y2R5//59AMCQIUO6bVdbWwsA2LhxI0QikfJVUlKCuro6rfuztrbG6dOnERAQgMTERHh5eSEkJAT19fV666MvsLKyQkVFhdBhMMaY3vXLZNlWteHZs2fdtmtLpikpKSAildf58+d16tPX1xfHjh1DaWkpoqOjkZGRge3bt+u1D1PW1NSEJ0+ewN3dXehQGGNM7/plshw7dizMzMxw5syZbtsNGzYMEomk1yv6lJaWorCwEMDzBPzpp59i4sSJKCws1Fsfpi4/Px9EBD8/P+U2sVis8fItY4z1Bf0yWQ4ZMgRBQUHIzs7G/v37oVAocO3aNezZs0elnUQiwdKlS3Hw4EGkpaVBoVCgpaUF9+/fx88//6x1f6WlpQgPD8eNGzfQ2NiIy5cvo6SkBH5+fnrrw9S0traiqqoKzc3NuHbtGiIjI+Hh4YElS5Yo2/j4+ODx48fIzc1FU1MTKioqUFJSorYvBwcHlJaWori4GNXV1WhqakJeXh5PHWGMmQ7BHsTVQm+mjlRXV9OyZcto8ODBNGjQIAoICKDNmzcTAHJ3d6erV68SEdGzZ88oOjqaPDw8SCwW05AhQygoKIgKCgpo9+7dJJVKCQCNHDmSioqKaM+ePSSXywkADR8+nG7dukXFxcXk7+9P9vb2ZG5uTkOHDqXY2Fhqbm7W2Ieu9DF1ZNeuXeTi4kIASCqV0ty5c7U+VqLnU0csLCzIzc2NxGIxyeVymjdvHhUVFan0U1lZSTNnziSJREKenp60atUqioqKIgDk4+OjnGZy6dIlGj58OFlbW1NAQACVlZXRiRMnSCaTUUJCQq+OtQ1M/9F0pgMez/6lD4xnpojIdBcJXbhwIQAgKytL4EhMR2ZmJhYtWiTo2q7h4eHIyspCZWWlYDHoSiQSISMjA2+99ZbQoTA94PHsX/rAeGb1y8uwzPBaWlqEDoExxoyGkyVjGnz77beIiYlBTk4OvLy8lNN/3sngjaoAACAASURBVH33XbW2r7zyCmQyGczNzeHr64tLly4JELH2ZsyYoTKlqf1r0KBBKm2/+uorTJ48GTKZDMOHD8fSpUtRVlbW7f4bGhowevRobNy4Ubnt6NGjSEpKEuwPrv48ngkJCZ2OZft53u21trYiJSUF/v7+nb4fHx+PMWPGQC6Xw8rKCj4+Pvj4449RU1OjbCP0eBqNwNeBu9Wbe5b9lb6Wu+upmJgYsrS0JAA0YsQIysrKEiwWXaCH90Q2b95Mc+bMIYVCodzm7e1NgwcPJgB0/Phxtc/k5eXRm2++2at4jSUwMJAAdPp69dVXle0OHTpEACgpKYmePHlCly9fJi8vL5owYQI1NTV1uf+1a9cSAIqNjVXZvnPnTgoMDKSqqqoexc3j2bktW7Z0Opa+vr5qbW/dukXTpk0jAPTSSy91ur/AwEDavXs3VVZWkkKhoIyMDLKwsKDXXntNpZ1Q42lE/XO5O2Y4W7duxbNnz0BE+OmnnxAcHCx0SAazbds2HDp0CJmZmZDJZCrvpaamwszMDGFhYSZT6qwnJBIJFAqF2hzgsLAwfPzxx8p2f/nLXzB06FBERUXB1tYWEyZMwNq1a3HlyhWVBfTbO3fuHH744YdO31u9ejVeeuklvPHGG2hubjbIsXU0EMYTAA4cOKA2nh3H4erVq1i/fj1WrFiBCRMmdLmvQYMGISwsDA4ODpDJZHjrrbcwf/58nDx5Evfu3VO2E2I8jY2TJWOduHPnDjZt2oRPPvlEuchFe/7+/oiMjMSDBw/w0UcfCRChfpw8eVItcdy7dw8//PADfvOb36hsc3V1VSlzN2zYMADodDpQfX09oqKisHPnzi77jouLw5UrV7ptoy8DZTy19dJLLyEnJweLFy+GlZVVl+2OHz8Oc3NzlW2Ojo4AoLYCmTHHUwicLBnrRGpqKogIc+fO7bJNQkICXnjhBezbtw/ffvttt/sjIuzYsUO5+Ly9vT3mzZunspauLiXhDFn2bdu2bVi9erXKNi8vL7Wao233K728vNT2ERsbi5UrV3a75KS9vT0CAwOxc+dOgz/dPZDHU98ePHgAa2treHp6qmw35ngKQoBrv1rje5bqhL5n2VdBx3siXl5eNGbMmE7f8/b2pp9++omIiM6dO0dmZmY0YsQIqqmpIaLO73Ft3ryZLC0t6cCBA/TkyRO6du0aTZw4kRwdHamsrEzZTtsyafos+9be/fv3acyYMdTS0qKyPT8/nywsLCg1NZUUCgX98MMP9OKLL6rc12xz9uxZmjt3LhERVVRUdHrPsk1MTIxa2Txt8Hh2bsuWLeTu7k52dnZkYWFBI0aMoDfffJP+53/+p8vP/OpXv+rynmVHtbW1JJPJKCIiotP3jTWeAuB7lox1VFtbi59++gne3t4a206dOhVr1qxBcXEx1q9f32mb+vp67NixAwsWLEBoaChsbW0xbtw4fPHFF3j06JHaylJA92XSDFn2bdu2bVi1ahXMzFR/NQQGBiI6OhoRERGQy+UYO3YsqqursW/fPrVjjYyMRFpamlb9jRw5EgBw/fr1XsXdnYE0nu+//z6OHj2Ke/fuoaamBgcPHsTdu3cRGBiIgoICnfbVma1bt8LV1RUJCQmdvm+M8RSKWOgANLl//z4yMzOFDsNktC2+zufEcMrLy0FEkEqlWrVPSEjA8ePHsXv3bixatEjt/YKCAtTU1GDSpEkq2ydPngxLS8suH5Bp07FMmqHKvpWWluLo0aNITk5Wey82Nhb79u3DqVOn8Ktf/Qrl5eVYv349pk6dinPnzinvX27YsAF/+MMf4ObmplWfbef44cOHPY5bk4E0nsOGDVOOBQD4+fkhPT0dEyZMwO7du7X+I6Yzhw8fRmZmJv75z3+q3eduY4zxFIrJJ8vvv/++0x/YgY7PieE0NDQAQLcPPrQnkUiQnp6OgIAAfPDBB0hKSlJ5/8mTJwCgNm8RAOzs7FBdXa1TfO3LvrWfvwgArq6uOu2rvaSkJCxfvlztAZiff/4ZSUlJiImJUT704+npib1798Le3h7JyclITU3F2bNncf36dezYsUPrPq2trQH8+5wbwkAdzzbjxo2Dubk5bt261eN9HDp0CDt27EB+fj6GDh3aZTtjjKdQTP4ybHBwsNpj0AP51XbTX+g4+tpLF23/4XWZZD116lSsXbsWt2/fxpYtW1Tes7OzA4BOf4n2pKyZIcq+lZWV4auvvsKHH36o9t7t27fR0tKi9ktSLpfDwcFBeXlv//79OHXqFMzMzJST4dtiTUxMhEgkwr/+9S+VfTQ2NgL49zk3hIE4nu21traitbVV6z8WOtq1axe+/PJLnD59uttECRhnPIVi8smSMWNzcnKCSCTSeb7dli1bMHr0aFy+fFll+9ixYzFo0CC1RHHhwgU0Njbil7/8pU79GKLsW1JSEkJDQ+Hg4KD2Xtsv/45Vcqqrq/H48WPlZb/09HS1X/ZtxcBjY2NBRGqXLtvOsbOzs96OpaOBNJ6vvvqq2raLFy+CiDB16lSd9kVEiI6OxvXr15Gbm9vpN+mOjDGeQuFkyVgHUqkUXl5euH//vk6fa7t813FemkQiwbp163D48GF8+eWXUCgUuH79OlasWAFXV1eEhYXp3I+msm8hISFwdnbWanm2hw8f4q9//SvWrFnT6fuenp6YOXMm9u7di++++w719fW4d++eMu7f//73OsXfXts5HjduXI/3oclAGs8HDx7g0KFDePLkCZqamnD+/HksW7YMHh4eWLFihU5xFRYW4rPPPsPevXthYWGhtoTe9u3b1T5jjPEUDJkwnjqijqeO9Ax0fDQ9IiKCLCwsqK6uTrnt8OHD5O3tTQDI0dGR/vjHP3b62aioKLWpBq2trZScnEwjR44kCwsLsre3p/nz59PNmzeVbXQpk6ap7Nv8+fMJAG3evFnjsa5du5ZCQ0O7bfPo0SOKjIwkHx8fsrKyokGDBtG0adPoH//4R7ef0zR1ZPbs2eTm5katra0a42yPx7Nz69atI29vb7KxsSGxWEzu7u60fPlyKi0tVWl3/vx5mjZtGrm6uiqXxHNxcSF/f386c+YMERFdv369y6UQAVBycrJa/8YaTwFkmvRvXU6W6jhZ9oyu/xlv375NYrGYDhw4YMCoDKelpYWmT59O+/fvFzqULj169IgkEglt375d58/yeJoeY46nAHieJWOd8fHxQXx8POLj41UqLPQFLS0tyM3NRXV1NUJCQoQOp0txcXGYMGECIiIiDN4Xj6fhGXM8hcDJkrEuxMTEYOHChQgJCelTi2vn5+cjJycHeXl5Ws8tNLYdO3bgypUrOHHiBCwsLIzSJ4+n4QgxnsbWr5Jlx/p0bS9LS0s4OTlhxowZSE5ORlVVldChsj4iMTERERER+PTTT4UORWuzZs3C3//+d7i4uAgdSqeOHDmCZ8+eIT8/H/b29kbtm8dT/4QcT2PqV8kyKCgIP/74I7y9vWFrawsiQmtrK8rLy5GZmQlPT09ER0fD19dX7bFvxrryyiuvYNu2bUKH0W+8+eabiImJUXvK1Fh4PPVL6PE0ln6VLDsjEolgZ2eHGTNmID09HZmZmXj48CFmz57dpy7FmJL6+vouK6v3pT4YY0xb/T5ZdhQcHIwlS5agvLwcX3zxhdDh9En79+9XK9fUF/tgjDFtDbhkCQBLliwBAOTl5Sm3dVdPTpe6dGfOnMGUKVMglUohl8sxbtw4KBQKjX0YEpHm2nsRERGwtLRUuS+ycuVK2NjYQCQS4dGjRwCAyMhIrFu3DkVFRRCJRPDx8UFqaiokEgmcnJwQHh4OV1dXSCQS+Pv7qywq3Zs+gOeFiuVyORITEw16vhhjTI3Qk1e609N5lt7e3mRra9vl+wqFggDQsGHDlNs01ZPTpi5dTU0NyeVySkpKovr6eiorK6MFCxZQRUWFVn1ooyfzLLWtvbd48WJydnZW+WxycjIBUB4DEVFQUBB5e3urtAsLCyMbGxsqLCykhoYGKigooMmTJ5NMJqO7d+/qpY/jx4+TTCaj+Ph4nY6fqE/M42I64PHsX/rAeA7MeZYymQwikUi5ELIu9eS6q0tXXFwMhUIBX19fSCQSODs7IycnB46OjgatQdidntTe6ymxWKz89jpmzBikpaWhurpab8c3e/ZsKBQKbNq0SS/7Y4wxbQ3IZFlbWwsiglwuB9DzenId69J5eXnByckJoaGhiIuLQ3FxsbKtoWoQatLb2nu9MWnSJEilUoMeH2OMGcOATJZtdd1Gjx4NQLWeXPv5mSUlJairq9N6v9bW1jh9+jQCAgKQmJgILy8vhISEoL6+Xm996Erftfd0ZWVlpaw8wRhjfdWATJYnT54EALz++usA9FtPztfXF8eOHUNpaSmio6ORkZGB7du3G7xmXVf0XXtPF01NTQbvgzHGjGHAJcuysjKkpKTA3d0dH3zwAQD91ZMrLS1FYWEhgOcJ+NNPP8XEiRNRWFhokBqE2tCl9p5YLFZeUtaH/Px8EBH8/PwM1gdjjBlDv02WRISamhq0trYqi9BmZGRg2rRpMDc3R25urvKepTb15LRRWlqK8PBw3LhxA42Njbh8+TJKSkrg5+entz50pUvtPR8fHzx+/Bi5ubloampCRUUFSkpK1Pbp4OCA0tJSFBcXo7q6Wpn8WltbUVVVhebmZly7dg2RkZHw8PBQTtXpbR95eXk8dYQxJgxhnsLVjq5TR44ePUrjx48nqVRKlpaWZGZmRgBIJBKRnZ0dTZkyheLj46myslLts93Vk9O2Ll1xcTH5+/uTvb09mZub09ChQyk2Npaam5s19qGtnkwd0ab2HhFRZWUlzZw5kyQSCXl6etKqVasoKiqKAJCPj49yCsilS5do+PDhZG1tTQEBAVRWVkZhYWFkYWFBbm5uJBaLSS6X07x586ioqEhvfZw4cYJkMhklJCTodPxEfeLRdKYDHs/+pQ+MZ6aIiEiwTK3BwoULAQBZWVkCR2I6MjMzsWjRIpjasIWHhyMrKwuVlZVCh9IpkUiEjIwMvPXWW0KHwvSAx7N/6QPjmdVvL8My42tpaRE6BMYYMwhOlowxxpgGnCxZr23YsAHp6el4+vQpPD09kZ2dLXRIjDGmV2KhA2B939atW7F161ahw2CMMYPhb5aMMcaYBpwsGWOMMQ04WTLGGGMacLJkjDHGNDD5B3y+//575eIEDLh//z4A8DnpgZSUFF7goh/h8WTGZNIr+OzYscOgFTkYMzVlZWW4fPmysiIOYwPF2rVrMXXqVKHD6EqWSSdLxgYaU13OkLEBjpe7Y4wxxjThZMkYY4xpwMmSMcYY04CTJWOMMaYBJ0vGGGNMA06WjDHGmAacLBljjDENOFkyxhhjGnCyZIwxxjTgZMkYY4xpwMmSMcYY04CTJWOMMaYBJ0vGGGNMA06WjDHGmAacLBljjDENOFkyxhhjGnCyZIwxxjTgZMkYY4xpwMmSMcYY04CTJWOMMaYBJ0vGGGNMA06WjDHGmAacLBljjDENOFkyxhhjGnCyZIwxxjTgZMkYY4xpwMmSMcYY04CTJWOMMaYBJ0vGGGNMA06WjDHGmAacLBljjDENOFkyxhhjGoiFDoCxgaqpqQk1NTUq22prawEAVVVVKttFIhHs7OyMFhtjTBUnS8YE8vjxY7i5uaGlpUXtPQcHB5V/z5w5E6dPnzZWaIyxDvgyLGMCcXZ2xq9//WuYmXX/31AkEuHtt982UlSMsc5wsmRMQO+++67GNubm5liwYIERomGMdYWTJWMCCgoKgljc9d0Qc3NzvPbaaxg8eLARo2KMdcTJkjEByeVyvP76610mTCJCaGiokaNijHXEyZIxgYWGhnb6kA8AWFpa4ne/+52RI2KMdcTJkjGB/e53v4NUKlXbbmFhgfnz58PGxkaAqBhj7XGyZExgEokECxYsgIWFhcr2pqYmLF68WKCoGGPtcbJkzAS88847aGpqUtkml8vx29/+VqCIGGPtcbJkzAS8/PLLKgsRWFhY4O2334alpaWAUTHG2nCyZMwEiMVivP3228pLsU1NTXjnnXcEjoox1oaTJWMm4u2331ZeinV2dkZAQIDAETHG2nCyZMxE+Pv7w83NDQDw3nvvaVwGjzFmPCa3kHpmZqbQITAmmMmTJ+PBgwcYPHgw/19gA9awYcMwdepUocNQISIiEjqI9kQikdAhMMYYE1BwcDCysrKEDqO9LJP7ZgkAGRkZeOutt4QOo99YuHAhAJjaD59Jy8zMxKJFiyDE35LZ2dkIDg42er/9mZDjyXTT9vvK1PBNEcZMDCdKxkwPJ0vGGGNMA06WjDHGmAacLBljjDENOFkyxhhjGnCyZIwxxjTod8ly2bJlkMlkEIlEuHLlitDh9EpraytSUlLg7+8vdCgAgBMnTsDW1hbHjh0TOhTGGDOqfpcs9+3bh7179wodRq/dvn0bv/71r7F27VrU1dUJHQ4A8Bw1xtiAZZKLEgx0V69eRXx8PFasWIHa2lqTSVKzZ8/G06dPhQ4DAFBfX49Zs2bh3LlzQofCGBsA+t03S6DvL5n30ksvIScnB4sXL4aVlZXQ4Zik/fv3o7y8XOgwGGMDRJ9PlkSE5ORkjBo1ClZWVrC1tUVUVJRau5aWFmzevBkeHh6wtrbG+PHjkZGRAQBIS0uDjY0NpFIpjhw5gtdffx1yuRzu7u44ePCgyn7OnDmDKVOmQCqVQi6XY9y4cVAoFBr76OvOnj0LDw8PiEQifP755wC0P2+pqamQSCRwcnJCeHg4XF1dIZFI4O/vjwsXLijbRUREwNLSEi4uLsptK1euhI2NDUQiER49egQAiIyMxLp161BUVASRSAQfHx8AwMmTJyGXy5GYmGiMU8IYG0D6fLLctGkToqOjERYWhocPH6KsrAzr169Xa7d+/Xp89tlnSElJwc8//4w5c+bgnXfewb/+9S98+OGHWLNmDerr6yGTyZCRkYGioiJ4eXlh+fLlyhqDtbW1mDt3LoKDg/H48WPcvn0bL7zwAhobGzX20dcFBASoXfLU9rxFRERgyZIlqKurw+rVq1FcXIxLly6hubkZv/3tb3Hv3j0Az5NqxzWBd+/ejU8++URl286dOzFnzhx4e3uDiHDnzh0Az/9YAZ4/GMUYY/rUp5NlfX09UlJS8PLLL2Pt2rWws7ODtbU1HBwcVNo1NDQgLS0N8+fPR1BQEOzs7LBx40ZYWFggPT1dpa2/vz/kcjmGDBmCkJAQ1NbW4u7duwCA4uJiKBQK+Pr6QiKRwNnZGTk5OXB0dNSpj/6ou/PWRiwW48UXX4SVlRXGjBmDtLQ0VFdX6+38zJ49GwqFAps2bdLL/hhjrE2fTpZ37txBXV0dZs2a1W27mzdvoq6uDmPHjlVus7a2houLC27cuNHl5ywtLQFA+Q3Jy8sLTk5OCA0NRVxcHIqLi3vdR3/U8bx1ZdKkSZBKpQPu/DDG+p4+nSzv378PABgyZEi37WprawEAGzduhEgkUr5KSkp0mpZhbW2N06dPIyAgAImJifDy8kJISAjq6+v11sdAY2VlhYqKCqHDYIyxbvXpZCmRSAAAz54967ZdWzJNSUkBEam8zp8/r1Ofvr6+OHbsGEpLSxEdHY2MjAxs375dr30MFE1NTXjy5Anc3d2FDoUxxrrVp5Pl2LFjYWZmhjNnznTbbtiwYZBIJL1e0ae0tBSFhYUAnifgTz/9FBMnTkRhYaHe+hhI8vPzQUTw8/NTbhOLxRov3zLGmLH16WQ5ZMgQBAUFITs7G/v374dCocC1a9ewZ88elXYSiQRLly7FwYMHkZaWBoVCgZaWFty/fx8///yz1v2VlpYiPDwcN27cQGNjIy5fvoySkhL4+fnprY/+rLW1FVVVVWhubsa1a9cQGRkJDw8PLFmyRNnGx8cHjx8/Rm5uLpqamlBRUYGSkhK1fTk4OKC0tBTFxcWorq5GU1MT8vLyeOoIY8wwyMQAoIyMDK3bV1dX07Jly2jw4ME0aNAgCggIoM2bNxMAcnd3p6tXrxIR0bNnzyg6Opo8PDxILBbTkCFDKCgoiAoKCmj37t0klUoJAI0cOZKKiopoz549JJfLCQANHz6cbt26RcXFxeTv70/29vZkbm5OQ4cOpdjYWGpubtbYhy7Onz9P06ZNI1dXVwJAAMjFxYX8/f3pzJkzOu2LiCg4OJiCg4N1/lx7u3btIhcXFwJAUqmU5s6dq/V5IyIKCwsjCwsLcnNzI7FYTHK5nObNm0dFRUUq/VRWVtLMmTNJIpGQp6cnrVq1iqKioggA+fj40N27d4mI6NKlSzR8+HCytramgIAAKisroxMnTpBMJqOEhIReHSsRUUZGBpngfw/WQzyefYc+fl8ZQKaIyETWUvv/RCIRMjIy1ObbsZ5buHAhACArK0uwGMLDw5GVlYXKykrBYtBFZmYmFi1aZDJLDbLe4fHsO0zh91Unsvr0ZVjWt7QtGsAYY30NJ0sjuHHjhsp0kq5eISEhQofK9OTbb79FTEwMcnJy4OXlpRzjd999V63tK6+8AplMBnNzc/j6+uLSpUsCRKy9hISETn9+288xbk9Tqbn4+HiMGTMGcrkcVlZW8PHxwccff4yamhplm6NHjyIpKUmwP7j683i20aYk4NmzZzFt2jRIpVK4uroiOjpaZTaC0ONkUMJeBlYHHe9ZMs2EvgcQExNDlpaWBIBGjBhBWVlZgsWird7c49q8eTPNmTOHFAqFcpu3tzcNHjyYANDx48fVPpOXl0dvvvlmj+M1pi1btijvpbd/+fr6qrW9desWTZs2jQDQSy+91On+AgMDaffu3VRZWUkKhYIyMjLIwsKCXnvtNZV2O3fupMDAQKqqqtI5Zh7P7mkzTj/88ANZW1vTpk2bqKamhs6dO0eOjo60dOlSlXa9GSci4X9fdSGTv1kyg9u6dSuePXsGIsJPP/2E4OBgoUMymG3btuHQoUPIzMyETCZTeS81NRVmZmYICwszmVJnPXXgwAG1+cQ//PCDSpurV69i/fr1WLFiBSZMmNDlvgYNGoSwsDA4ODhAJpPhrbfewvz583Hy5EnlusEAsHr1arz00kt444030NzcbLBja28gjKe247Rlyxa4uLjgk08+gY2NDaZOnYro6Gj87W9/U1mFS4hxMgZOlozpyZ07d7Bp0yZ88sknygUz2vP390dkZCQePHiAjz76SIAIjUvbUnPHjx+Hubm5yjZHR0cAUFv9Ki4uDleuXMHOnTv1H3AHA2U8tRmn5uZmfP311wgMDFQpgfj666+DiHDkyBGV9sYcJ2PhZMmYnqSmpoKIMHfu3C7bJCQk4IUXXsC+ffvw7bffdrs/IsKOHTuUi8/b29tj3rx5Kn/F61Jeri+VkHvw4AGsra3h6empst3e3h6BgYHYuXOnwZ9s5fH8tx9//BE1NTXw8PBQ2e7t7Q0AuHbtmsp2Y46TsXCyZExPvv76a4waNQpSqbTLNtbW1vjb3/4GMzMzLF++XLmmcGfi4uIQExOD2NhYlJeX47vvvsO9e/cwffp0PHz4EID2ZdIA/ZaQi4mJgb29PSwtLeHp6Yl58+bh4sWLOu+nM3V1dTh9+jSWL1+uXJS/vV/84hd48OABrl69qpf+ujKQxlOTsrIyAFC7FC2RSGBtba2Mvz1jjZOxcLJkTA9qa2vx008/Kf/S7s7UqVOxZs0aFBcXd1p7FXhefm7Hjh1YsGABQkNDYWtri3HjxuGLL77Ao0eP1FapArovk6bPEnLvv/8+jh49inv37qGmpgYHDx7E3bt3ERgYiIKCAp321ZmtW7fC1dUVCQkJnb4/cuRIAMD169d73VdXBtJ4aqPtideOl8sBwMLCAvX19WrbjTFOxiQWOoDOpKSkmNqE1D7t+++/B/Dvyb5Ms7aKNtoqLy8HEXX7LaS9hIQEHD9+HLt378aiRYvU3i8oKEBNTQ0mTZqksn3y5MmwtLTEhQsXut1/xzJp+iwhN2zYMAwbNkz5bz8/P6Snp2PChAnYvXs30tLSdNpfe4cPH0ZmZib++c9/qn2LadN2jjv7NqMvA2k8tdF2z7azB3YaGxthbW2ttt0Y42RM/M2SMT1oaGgAgG4fZGlPIpEgPT0dIpEIH3zwgdpf5k+ePAHw/EnRjuzs7FBdXa1TfIYuITdu3DiYm5vj1q1bPd7HoUOHsG3bNuTn52PEiBFdtmv7xdx2zg1hoI9nRy4uLgAAhUKhsr2urg4NDQ1wdXVV+4wxxsmYTPKb5Zo1a3i5Oz0y0eWjTFrb8mjaavvFoMtk7KlTp2Lt2rXYvn07tmzZovLwhJ2dHQB0+ku0J2XN2peQi4yM1Omz2mhtbUVra6vWyaWjXbt24ZtvvsHp06c7TSjtNTY2AkCn32b0ZaCPZ0eenp6QyWRqRQ3u3LkDABg/frzaZ4wxTsbE3ywZ0wMnJyeIRCKd59tt2bIFo0ePxuXLl1W2jx07FoMGDVJ7WOPChQtobGzEL3/5S5360WcJuVdffVVt28WLF0FEmDp1qk77IiJER0fj+vXryM3N1ZgoASjPsbOzs0596WIgjac2xGIx3njjDXz33XdobW1Vbs/Ly4NIJOr0iWFjjJMxcbJkTA+kUim8vLx0vtfZdvmu44MTEokE69atw+HDh/Hll19CoVDg+vXrWLFiBVxdXREWFqZzP5pKyIWEhMDZ2Vnj8mwPHjzAoUOH8OTJEzQ1NeH8+fNYtmwZPDw8sGLFCp3iKiwsxGeffYa9e/fCwsJCbQm97du3q32m7RyPGzdOp750MZDGU1ubNm3Cw4cP8ac//Qm1tbU4f/48kpOTsWTJEowaNUqtvTHGyaiMv2pQ98DL3emdiS4fZdJ6sjxaREQEWVhYUF1dnXLb4cOHydvbmwCQo6Mj/fGPf+z0s1FRUWrLo7W2tlJycjKNHDmSLCwsyN7enubPn083b95UttGlTJqmmyl8xwAABx1JREFUEnLz588nALR58+Zuj3PdunXk7e1NNjY2JBaLyd3dnZYvX06lpaUq7bQpNXf9+vVOl85reyUnJ6v1P3v2bHJzc6PW1tZu42yPx7NrupQEPHPmDE2ZMoWsrKzI1dWVoqKiqKGhodP99mSciEz291UmJ8sBwER/+ExaT3653r59m8RiMR04cMBAURlWS0sLTZ8+nfbv3y90KF169OgRSSQS2r59u06f4/E0rp6OE5HJ/r7itWEZ0xcfHx/Ex8cjPj5epWJGX9DS0oLc3FxUV1ebdPWbuLg4TJgwAREREQbvi8ez54w5TsbSr5Nlx3I6bS9LS0s4OTlhxowZSE5ORlVVldChsn4iJiYGCxcuREhISJ9aXDs/Px85OTnIy8vTem6hse3YsQNXrlzBiRMnYGFhYZQ+eTx1J8Q4GUO/TpZBQUH48ccf4e3tDVtbWxARWltbUV5ejszMTHh6eiI6Ohq+vr4GWSKKDUyJiYmIiIjAp59+KnQoWps1axb+/ve/K+fTmZojR47g2bNnyM/Ph729vVH75vHUnpDjZGj9Oll2RiQSwc7ODjNmzEB6ejoyMzPx8OFDzJ49u0/95djX1NfXd1tUtq/0oa1XXnkF27ZtEzqMfuPNN99ETExMp8utGQOPp3aEHidDGnDJsqPg4GAsWbIE5eXl+OKLL4QOp9/av38/ysvL+3wfjLGBacAnSwBYsmQJgOcTbNt0V/5GlzI6Z86cwZQpUyCVSiGXyzFu3DjlklGmXDKJtCgnFBERAUtLS5VLPStXroSNjQ1EIhEePXoEAIiMjMS6detQVFQEkUgEHx8fpKamQiKRwMnJCeHh4XB1dYVEIoG/v7/KOpm96QMATp48CblcjsTERIOeL8ZYPyf087gdwQBTR7y9vcnW1rbL9xUKBQGgYcOGKbd99NFHZGVlRdnZ2VRVVUUbNmwgMzMzunjxIhERxcbGEgA6deoUPX36lMrLy2n69OlkY2NDjY2NRERUU1NDcrmckpKSqL6+nsrKymjBggVUUVGhVR/60pNHsTdv3kyWlpZ04MABevLkCV27do0mTpxIjo6OVFZWpmy3ePFicnZ2VvlscnIyAVAeJxFRUFAQeXt7q7QLCwsjGxsbKiwspIaGBiooKKDJkyeTTCaju3fv6qWP48ePk0wmo/j4eJ2OvydTDZjp4vHsO3jqiAmTyWQQiUTKdRt1KX/TXRmd4uJiKBQK+Pr6QiKRwNnZGTk5OXB0dDR6iR1d9KScUE+JxWLlt9cxY8YgLS0N1dXVejsHs2fPhkKhwKZNm/SyP8bYwMTJEs9X8CciyOVyAD0vf9OxjI6XlxecnJwQGhqKuLg4FBcXK9sau8SOLnpbTqg3Jk2aBKlUKvg5YIyx9jhZAsqyQqNHjwagv/I31tbWOH36NAICApCYmAgvLy+EhISgvr7e6CV2dKHvckK6srKyQkVFhUH7YIwxXXCyxPOHQADg9ddfB6Ba/oaIVF7nz5/Xad++vr44duwYSktLER0djYyMDGzfvl2vfeibvssJ6aKpqcngfTDGmK4GfLIsKytDSkoK3N3d8cEHHwDQX/mb0tJSFBYWAniegD/99FNMnDgRhYWFRi+xowtdygmJxWLlZWd9yM/PBxHBz8/PYH0wxpiuBkyyJCLU1NSgtbUVRISKigpkZGRg2rRpMDc3R25urvKepTblb7RRWlqK8PBw3LhxA42Njbh8+TJKSkrg5+entz4MQZdyQj4+Pnj8+DFyc3PR1NSEiooKtQKxAODg4IDS0lIUFxejurpamfxaW1tRVVWF5uZmXLt2DZGRkfDw8FBO5+ltH3l5eTx1hDHWe8I8hds16HHqyNGjR2n8+PEklUrJ0tKSzMzMCACJRCKys7OjKVOmUHx8PFVWVqp9trvyN9qW0SkuLiZ/f3+yt7cnc3NzGjp0KMXGxlJzc7PGPvSpJ49ia1NOiIiosrKSZs6cSRKJhDw9PWnVqlUUFRX1/9q5YxQHgSiM40/QIkVyAQkhkGN4CIvEHEHPYB3mGtaTsfYMW+UG9jYpcoDw0i0sYZndZWEm8f+7gJ8M+jHiGxUR3e12nyMgl8tFN5uNLhYLLYpCp2nSuq41yzLN81zTNNXVaqVlWeo4jv92jWEYdLlc6ul0+tX9M2rwXljP1xHr6Eiiqhquqp8lSSLWWqmqKnSUt3E4HERExDkXOMlXTdOIc06u12voKE/O57Mcj0eJ7PHAH7GeryPS95WbzWdYxOl+v4eOAABelCUAAB6UJYJo21a6rpPb7Sbb7Vb6vg8dCQC+lYYOgHkyxogxJnQMAPgRdpYAAHhQlgAAeFCWAAB4UJYAAHhQlgAAeER5gg8AYL72+310J/hENzpirQ0dAQAQ0Hq9Dh3hSXQ7SwAAIsPZsAAA+FCWAAB4UJYAAHikIhLVL0cAAETm4wF3vrN+R7esIQAAAABJRU5ErkJggg==\n"
          },
          "metadata": {},
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(model.summary())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "orXMosZZUg2l",
        "outputId": "f656c4bb-5898-41c3-de12-1a3eb13dc744"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model: \"sequential\"\n",
            "_________________________________________________________________\n",
            " Layer (type)                Output Shape              Param #   \n",
            "=================================================================\n",
            " dense (Dense)               (None, 512)               401920    \n",
            "                                                                 \n",
            " dense_1 (Dense)             (None, 10)                5130      \n",
            "                                                                 \n",
            "=================================================================\n",
            "Total params: 407,050\n",
            "Trainable params: 407,050\n",
            "Non-trainable params: 0\n",
            "_________________________________________________________________\n",
            "None\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sm6_pZt9ugVt"
      },
      "source": [
        "**Hacer predicciones con nuestro modelo**\n",
        "\n",
        "Una vez el modelo ha sido ajustado/entrenado podemos utilizarlo para predecir las propbabilidades de nuevos dígitos que no fueron utilizados durante el entrenamiento y reservamos en el conjunto de *test*. \n",
        "\n",
        "En el siguente código cada posición `i` del vector de predicciones corresponde a la probabilidad de que la imagen `test_digits[0]` pertenezca a la clase `i`."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MqVcR54bugVt",
        "outputId": "1d3a12f4-158a-4571-edfc-cf0f31f04a43"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1.4680411e-08, 2.9098512e-09, 1.0566339e-05, 1.5245122e-04,\n",
              "       1.5660423e-12, 3.2530198e-07, 3.0141365e-13, 9.9983490e-01,\n",
              "       7.0689401e-07, 9.2617421e-07], dtype=float32)"
            ]
          },
          "metadata": {},
          "execution_count": 16
        }
      ],
      "source": [
        "test_digits = test_images[0:10]\n",
        "predictions = model.predict(test_digits)\n",
        "predictions[0]"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Para este primer patrón de test, el índice `i` con mayor probabilidad, `0.99999106` para `7` en nuestro caso, es la clase estimada por nuestro modelo, por tanto debe ser un 7."
      ],
      "metadata": {
        "id": "eBCeS1zgXTIu"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "yZNubECpugVu",
        "outputId": "898ca6ad-8595-4bff-894a-e33ec322273c"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "7"
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ],
      "source": [
        "predictions[0].argmax()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "AYASOpE_ugVu",
        "outputId": "2982bca2-6a3e-4778-949d-0832ff9310b7"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.9998349"
            ]
          },
          "metadata": {},
          "execution_count": 18
        }
      ],
      "source": [
        "predictions[0][7]"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Podemos constrastar la preducción con la etiqueta del patrón:"
      ],
      "metadata": {
        "id": "XH1gbs-oYPe2"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0NTp-tsLugVv",
        "outputId": "1e4983a8-31af-4827-931c-b0ae1f1d791a"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "7"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ],
      "source": [
        "test_labels[0]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aPRW3h7rugVw"
      },
      "source": [
        "**Evaluación del modelo**\n",
        "\n",
        "Podemos calcular la precisión global media sobre todo el conjunto de *test*. En  este caso la precisión es ligeramente inferior a la de entrenamiento. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "lcjL_2KyugVw",
        "outputId": "4e9402a4-311b-4a96-e640-a1b570034e28"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "313/313 [==============================] - 1s 2ms/step - loss: 0.0650 - accuracy: 0.9804\n",
            "test_acc: 0.980400025844574\n"
          ]
        }
      ],
      "source": [
        "test_loss, test_acc = model.evaluate(test_images, test_labels)\n",
        "print(f\"test_acc: {test_acc}\")"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "test_pred = model.predict(test_images)"
      ],
      "metadata": {
        "id": "x52is0NnaZ7z"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "test_pred = test_pred.argmax(axis=1)"
      ],
      "metadata": {
        "id": "QwQX1jiWb1yv"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.metrics import classification_report, confusion_matrix\n",
        "confusion_matrix(test_labels, test_pred)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "r67zvcJPd76l",
        "outputId": "1c2f4a61-a477-47b4-dd01-a0f6ebc28006"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 972,    0,    1,    0,    0,    0,    3,    1,    3,    0],\n",
              "       [   0, 1126,    3,    0,    0,    0,    3,    0,    3,    0],\n",
              "       [   6,    1, 1012,    2,    1,    0,    2,    4,    4,    0],\n",
              "       [   0,    0,    1,  997,    0,    2,    0,    4,    3,    3],\n",
              "       [   4,    0,    5,    0,  950,    0,    3,    4,    3,   13],\n",
              "       [   3,    0,    0,    6,    1,  874,    3,    0,    4,    1],\n",
              "       [   5,    3,    1,    1,    2,    4,  941,    1,    0,    0],\n",
              "       [   2,    5,    7,    2,    0,    0,    0, 1003,    4,    5],\n",
              "       [   6,    0,    4,    5,    3,    2,    2,    2,  947,    3],\n",
              "       [   3,    4,    0,    7,    6,    1,    0,    4,    2,  982]])"
            ]
          },
          "metadata": {},
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7oWvf7ubugVx"
      },
      "source": [
        "## Data representations for neural networks\n",
        "\n",
        "Los tensores o *tensors* son el tipo de estructura de datos básico en aprendizaje máquina y en aprendizaje profundo en particular.\n",
        "\n",
        "Un tensor es un contenedor de datos, habitualmente numéricos. Ejemplos que ya conocemos son las matrices, que son tensores de orden-2 o rango-2 (*rank-2 tensors*). Los tensores son una generalización de las mastrices a un número arbitrario de *dimensiones*, que en el contexto de los tensores se llaman *ejes*.\n",
        "\n",
        "**Nota de traducción**: *rank* ~ orden, grado o rango."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mnzqUPzwugVx"
      },
      "source": [
        "### Escalares (rank-0 tensors)"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Un tensor de un sólo número se llama *escalar* o tensor de rango-0 o tensor 0D (`ndim == 0`)."
      ],
      "metadata": {
        "id": "Wlthqt8PiWAJ"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "m79bHmTrugVx",
        "outputId": "869a1363-40df-4786-fdea-20bcd29ecef1"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array(12)"
            ]
          },
          "metadata": {},
          "execution_count": 24
        }
      ],
      "source": [
        "import numpy as np\n",
        "x = np.array(12)\n",
        "x"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "FwxFYAGFugVy",
        "outputId": "2b7ef5a5-92a5-4fae-ac64-823e52c3c504"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0"
            ]
          },
          "metadata": {},
          "execution_count": 25
        }
      ],
      "source": [
        "x.ndim"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wNRiFcpVugVy"
      },
      "source": [
        "### Vectores (rank-1 tensors)\n",
        "\n",
        "Una matriz de números se llama vector, tensor de orden-1 o tensor 1D. Estos sólo tienen un eje:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "kDlMvu5BugVy",
        "outputId": "4e8dcbe9-5bfb-409d-d57b-877213154ecd"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([12,  3,  6, 14,  7])"
            ]
          },
          "metadata": {},
          "execution_count": 26
        }
      ],
      "source": [
        "x = np.array([12, 3, 6, 14, 7])\n",
        "x"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "UHFOzgJ7ugVz",
        "outputId": "dd8266ed-1a34-4762-86cc-9ef6ed0f4629"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1"
            ]
          },
          "metadata": {},
          "execution_count": 27
        }
      ],
      "source": [
        "x.ndim"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Decimos que este vector tiene 5 entradas y se llama vector de 5 dimensiones. No debemos confundir un vector 5D con un tensor 5D. Un vector sólo tiene un eje y tiene 5 dimensiones en él mientras que un tensor 5D tiene 5 ejes y cada eje particular puede tener cualquier número de dimensiones."
      ],
      "metadata": {
        "id": "6doixr9gjaV7"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gYTUGPynugV0"
      },
      "source": [
        "### Matrices (rank-2 tensors)\n",
        "\n",
        "Una matriz es un tensor de orden-2 o 2D que tiene 2 ejes que habitualmente llamanos filas y columnas. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7xqlf4PJugV0",
        "outputId": "5a30dde4-dccb-4df3-d35d-e3dd705dbaf5"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "2"
            ]
          },
          "metadata": {},
          "execution_count": 28
        }
      ],
      "source": [
        "x = np.array([[5, 78, 2, 34, 0],\n",
        "              [6, 79, 3, 35, 1],\n",
        "              [7, 80, 4, 36, 2]])\n",
        "x.ndim"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lkLCPdgpugV1"
      },
      "source": [
        "### Tensores de orden 3 o superior\n",
        "\n",
        "Si agrupamos varias matrices en un vector obtenemos un tensor de orden 3 o 3D que podemos interpretar como un cubo de números. Por ejemplo: \n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Xl5km1f0ugV1",
        "outputId": "2032f403-ec21-4c94-bb2f-1c411aab57da"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "3"
            ]
          },
          "metadata": {},
          "execution_count": 29
        }
      ],
      "source": [
        "x = np.array([[[5, 78, 2, 34, 0],\n",
        "               [6, 79, 3, 35, 1],\n",
        "               [7, 80, 4, 36, 2]],\n",
        "              [[5, 78, 2, 34, 0],\n",
        "               [6, 79, 3, 35, 1],\n",
        "               [7, 80, 4, 36, 2]],\n",
        "              [[5, 78, 2, 34, 0],\n",
        "               [6, 79, 3, 35, 1],\n",
        "               [7, 80, 4, 36, 2]]])\n",
        "x.ndim"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Si agrupamos tensores de orden 3 en otro vector crearemos un tensor de orden 4.\n",
        "\n",
        "En aprendizaje profundo lo habitual será trabajar con tensores de orden 0 al 4 o de orden 5 para procesar datos de vídeo."
      ],
      "metadata": {
        "id": "lDGWZ0z3kuS1"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DI4fPjfdugV1"
      },
      "source": [
        "### Propiedades clave de los tensores\n",
        "\n",
        "Un tensor queda definido por tres atributos clave: \n",
        "* Número de ejes (orden o rango o *rank*).\n",
        "* Forma (*shape*): tupla de enteros que describe cuántas dimensiones hay en cada eje. En los ejemplos anteriores: \n",
        "** escalar: forma vacía `()`\n",
        "** vector: forma con un único elemento `(5,)`\n",
        "** matriz: `(3, 5)` \n",
        "** tensor orden 3: `(3, 3, 5)` \n",
        "* Tipo de datos (`dtype` en las bibliotecas de Python): `float16`, `float32`, `float64`, `uint8`, etc. y `string` en TensorFlow.\n",
        "\n",
        "En nuestro conjunto de datos MINST: "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "fvX7xG4gugV2"
      },
      "outputs": [],
      "source": [
        "from tensorflow.keras.datasets import mnist\n",
        "(train_images, train_labels), (test_images, test_labels) = mnist.load_data()"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Podemos mostrar el número de ejes, la forma y tipo de datos del tensor `train_images` con el atributo `ndim`, `shape` y `dtype`:"
      ],
      "metadata": {
        "id": "5S3VSczKml9d"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Q3NEFBYrugV2",
        "outputId": "63fdc659-61cb-4dba-be8c-09f0d1cef111"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "3"
            ]
          },
          "metadata": {},
          "execution_count": 31
        }
      ],
      "source": [
        "train_images.ndim"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "HFZOYtLEugV3",
        "outputId": "b9fbd624-a750-4f5f-fadd-89905855fa03"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(60000, 28, 28)"
            ]
          },
          "metadata": {},
          "execution_count": 32
        }
      ],
      "source": [
        "train_images.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "eoJkXGJAugV3",
        "outputId": "146f1501-7465-4cf0-a983-e9fbc6bba0ae"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "dtype('uint8')"
            ]
          },
          "metadata": {},
          "execution_count": 33
        }
      ],
      "source": [
        "train_images.dtype"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Esto es, tenemos un tensor de orden 3 de enteros de 8 bits compuesto de un vector de 60.000 matrices de 28x28 enteros. Cada matriz es una imagen en escala de grises con coeficientes entre 0 y 255"
      ],
      "metadata": {
        "id": "ERSq5m7jpVQT"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FVaBKEsmugV3"
      },
      "source": [
        "Podemos ver las imágenes de cada patrón a través de `matplotlib`."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "AZOIHs5RugV3",
        "outputId": "fd3ae89a-4008-4ec3-f73f-9d7165dd3e66"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "import matplotlib.pyplot as plt\n",
        "digit = train_images[4]\n",
        "plt.imshow(digit, cmap=plt.cm.binary)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "W2UWzHIsugV4",
        "outputId": "aee41a11-8800-42d3-e476-996874f7c461"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "9"
            ]
          },
          "metadata": {},
          "execution_count": 35
        }
      ],
      "source": [
        "train_labels[4]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6sdY2VR8ugV4"
      },
      "source": [
        "### Manipulación de tensores en NumPy\n",
        "\n",
        "A la selección de elementos de un tensor se le llama *tensor slicing*. Algunos ejemplos.\n",
        "\n",
        "Seleccionar dígitos del #10 al #100 (#100 no incluído) y guardarlos en una matriz de forma `(90, 28, 28)`:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SPlqcS36ugV5",
        "outputId": "da646d67-9b62-4e48-8ec4-db08899cb509"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(90, 28, 28)"
            ]
          },
          "metadata": {},
          "execution_count": 36
        }
      ],
      "source": [
        "my_slice = train_images[10:100]\n",
        "my_slice.shape"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Expresión equivalente especificando los índices de inicio y fin para cada eje del tensor (`:` equivale a seleccionar un eje entero)."
      ],
      "metadata": {
        "id": "KBncddZhskDW"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Z9js9CIeugV5",
        "outputId": "ad2f4d0b-6144-48e2-e28d-fe9883f7ae08"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(90, 28, 28)"
            ]
          },
          "metadata": {},
          "execution_count": 37
        }
      ],
      "source": [
        "my_slice = train_images[10:100, :, :]\n",
        "my_slice.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ZJR4hDVSugV6",
        "outputId": "6c97d3b2-2cbd-42f1-b4db-941d0142e3cc"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(90, 28, 28)"
            ]
          },
          "metadata": {},
          "execution_count": 38
        }
      ],
      "source": [
        "my_slice = train_images[10:100, 0:28, 0:28]\n",
        "my_slice.shape"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "En general se pueden seleccionar trozos de un tensor entre dos índices de cada eje, por ejemplo, para seleccionar una zona de 14x14 píxeles de la esquina inferior derecha de todas las imágenes:"
      ],
      "metadata": {
        "id": "hdnl3Jqts34V"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "0Ac7j63HugV6"
      },
      "outputs": [],
      "source": [
        "my_slice = train_images[:, 14:, 14:]"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Visualizamos el dígito y su recorte: "
      ],
      "metadata": {
        "id": "AjU9PU3PtSMX"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "digit = train_images[4]\n",
        "plt.imshow(digit, cmap=plt.cm.binary)\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "w21g6hRKtXPL",
        "outputId": "e294cb03-5c7e-442f-89a9-f88ab02ff50e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "digit = my_slice[4]\n",
        "plt.imshow(digit, cmap=plt.cm.binary)\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "deeRZPEhtO6X",
        "outputId": "cf8e22e2-a7ce-4fe2-8615-d933fc9793d9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Se pueden utilizar índices negativos, que indican una posición relativa al final del eje. Por ejemplo, así recortaríamos las imágenes en áreas de 14x14 píxeles centrales: "
      ],
      "metadata": {
        "id": "4Hhqy9KAtcfy"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "h4rWW8hTugV7"
      },
      "outputs": [],
      "source": [
        "my_slice = train_images[:, 7:-7, 7:-7]"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "digit = my_slice[4]\n",
        "plt.imshow(digit, cmap=plt.cm.binary)\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "Z5xPIQVrt2_G",
        "outputId": "795bc56e-fdd1-431c-d910-7c5c98e84983"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ro_Izz-ZugV7"
      },
      "source": [
        "### Los lotes de datos (*data batches*)"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "En general, el primer eje (eje 0) en los tensores suele corresponde al eje/dimensión de los patrones o muestras. Los modelos de aprendizaje profundo no procesan conjuntos enteros de datos de una vez, sino que los parten en varios lotes. Un ejemplo de un lote de datos de tamaño 128 en MNIST:"
      ],
      "metadata": {
        "id": "1oQAC9kzvjAx"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "W-tkgpnVugV7"
      },
      "outputs": [],
      "source": [
        "batch = train_images[:128]"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Siguientes lotes: "
      ],
      "metadata": {
        "id": "fDdxbVFVwE0Q"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "4eaZiBE7ugV8"
      },
      "outputs": [],
      "source": [
        "batch = train_images[128:256]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "wWmmTHKrugV8"
      },
      "outputs": [],
      "source": [
        "n = 3\n",
        "batch = train_images[128 * n:128 * (n + 1)]"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "En Keras y otras herramientas se suele referir al eje 0 de estos lotes como *eje/dimensión del lote*."
      ],
      "metadata": {
        "id": "hRl8WmK-wOht"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "h-75bXODugV9"
      },
      "source": [
        "### Ejemplos reales de tensores de datos\n",
        "\n",
        "Algunos ejemplos típicos que encontraremos: \n",
        "* **Vectores de datos**: tensores de orden 2 `(samples, features)` donde cada patrón es un vector de atributos numéricos ('features').\n",
        "\n",
        "* **Series temporales o secuencias de datos**: tensores de orden 3 `(samples, timesteps, features)` donde cada muestra es una secuencia de longiud `timesteps` de vectores de atributos.\n",
        "* **Imágenes**: tensores de orden 4 `(samples, height, width, channels)` donde cada muestra se compone de tensores 2D de píxeles, y ada pixel está representado por un vector de varios valores ('canales')."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IUDApdWKugV9"
      },
      "source": [
        "### Datos de vectores\n",
        "\n",
        " * Datos tabulares de personas (edad, género, renta): `(100000, 3)`\n",
        " * Documentos representados por diccionario de aparición/frecuencia de palabras."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "55yZ_RxhugV-"
      },
      "source": [
        "### Series temporales y secuencias\n",
        "\n",
        "Tensor de orden 3 compuesto de una secuencia tensores de orden 2. Ejemplos: datos de precio de acciones donde se guardan 3 valores por minuto, cada día será una matriz `(390, 3)` y 250 días al año se pueden guardar en un tensor de orden 3 `(250, 390, 3)`.\n",
        "\n",
        "[Fuente imagen Collet 2022]\n",
        "![imagen.png](data:image/png;base64,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)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XGoYDsBTugV-"
      },
      "source": [
        "### Image data\n",
        "\n",
        "Tensor de orden 4: 128 imágenes de 256x256 píxeles y 3 canales `(128, 256, 256, 3)`\n",
        "\n",
        "[Fuente imagen Collet 2022]\n",
        "![imagen.png](data:image/png;base64,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)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "22p44_8pugV_"
      },
      "source": [
        "### Video data\n",
        "\n",
        "Un vídeo es una secuencia de fotogramas, que representan con tensores orden 3 `(height, width, color_ depth)`, una secuencia de fotogramas es un tensor de orden 4 `(frames, height, width, color_depth)`. Un lote de vídeos se puede almacenar en un tensor de orden 5 `(samples, frames, height, width, color_depth)` (ej `(4, 240, 144, 256, 3)`)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LWiQ6T56ugWA"
      },
      "source": [
        "## Operaciones con tensores\n",
        "\n",
        "Una capa del tipo que hemos definido:"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "keras.layers.Dense(512, activation=\"relu\")"
      ],
      "metadata": {
        "id": "Bah5Y3A4EwCF",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f803bb3a-e407-4772-9b36-1c020e94475b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<keras.layers.core.dense.Dense at 0x7efff7b9ea90>"
            ]
          },
          "metadata": {},
          "execution_count": 47
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Se puede interpretar como una función que toma una matriz como entrada y devuelve otra de salida: \n",
        "\n",
        "```\n",
        "output = relu(dot(input, W) + b)\n",
        "```\n",
        "\n"
      ],
      "metadata": {
        "id": "tpP-cTlwEw--"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Esta función se descompone en tres operaciones con tensores: \n",
        "* Producto escalar `dot`\n",
        "* Suma `+`\n",
        "* Operación `relu` (*rectified linear unit*): `max(x, 0)`\n",
        "\n",
        "[Fuente [Rectifier_(neural_networks) en Wikipedia](https://en.wikipedia.org/wiki/Rectifier_\\(neural_networks\\))]\n",
        "![imagen.png](data:image/png;base64,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)"
      ],
      "metadata": {
        "id": "Vl-0YLJ6E5Nc"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-t3audezugWA"
      },
      "source": [
        "### Operaciones por elementos\n",
        "\n",
        "Cómo sumar un vector a una matriz. Implementación no vectorizada/paralelizable vs optimizada por NumPy."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "arXZTkgOugWA"
      },
      "outputs": [],
      "source": [
        "def naive_relu(x):\n",
        "    assert len(x.shape) == 2\n",
        "    x = x.copy()\n",
        "    for i in range(x.shape[0]):\n",
        "        for j in range(x.shape[1]):\n",
        "            x[i, j] = max(x[i, j], 0)\n",
        "    return x"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "0_qh9-98ugWB"
      },
      "outputs": [],
      "source": [
        "def naive_add(x, y):\n",
        "    assert len(x.shape) == 2\n",
        "    assert x.shape == y.shape\n",
        "    x = x.copy()\n",
        "    for i in range(x.shape[0]):\n",
        "        for j in range(x.shape[1]):\n",
        "            x[i, j] += y[i, j]\n",
        "    return x"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9PglC12IugWB",
        "outputId": "4189633f-2a91-48bf-ce2c-0a40a9633257"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Took: 0.01 s\n"
          ]
        }
      ],
      "source": [
        "import time\n",
        "\n",
        "x = np.random.random((20, 100))\n",
        "y = np.random.random((20, 100))\n",
        "\n",
        "t0 = time.time()\n",
        "for _ in range(1000):\n",
        "    z = x + y\n",
        "    z = np.maximum(z, 0.)\n",
        "print(\"Took: {0:.2f} s\".format(time.time() - t0))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 133
        },
        "id": "-SJQ7QuQugWB",
        "outputId": "7cfc3169-558b-4788-aba4-107573e6bcca"
      },
      "outputs": [
        {
          "output_type": "error",
          "ename": "SyntaxError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;36m  File \u001b[0;32m\"<ipython-input-53-c46538814482>\"\u001b[0;36m, line \u001b[0;32m1\u001b[0m\n\u001b[0;31m    0 = time.time()\u001b[0m\n\u001b[0m                   ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m can't assign to literal\n"
          ]
        }
      ],
      "source": [
        "0 = time.time()\n",
        "for _ in range(1000):\n",
        "    z = naive_add(x, y)\n",
        "    z = naive_relu(z)\n",
        "print(\"Took: {0:.2f} s\".format(time.time() - t0))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IPC82FxkugWB"
      },
      "source": [
        "### Broadcasting"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Las funciones anteriores sólo permiten operaciones con tensores 2D con formas idénticas, es decir, no pueden sumar, por ejemplo, una matriz y un vector. \n",
        "\n",
        "Si los tamaños difieren y no hay ambigüedad, el tensor más pequeño se *emite*/*reforma* para encajar con la forma del tensor mayor. Esto consiste en dos pasos: \n",
        "1. Se añaden ejes al tensor menor para que tenga la misma `ndim` del mayor.\n",
        "1. Se repite el tensor a lo largo de los nuevos ejes hasta alcanzar la forma completa del tensor. \n",
        "\n",
        "Algunas de estas operaciones seán automatizadas por Keras para evitar tener que programar explícitamente las formas de las capas de la red para que sean compatibles entre si. "
      ],
      "metadata": {
        "id": "GO9R7O-MGdwy"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Tz8bvvV8ugWB"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "X = np.random.random((32, 10))\n",
        "y = np.random.random((10,))"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Añadimos un eje vacío al vector `y`:"
      ],
      "metadata": {
        "id": "Jd1VvlLYDL3o"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "YkIu4ETYugWC",
        "outputId": "f8d1bd2a-1c1f-45bb-b996-15b12de00edc"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(10,)\n",
            "(1, 10)\n"
          ]
        }
      ],
      "source": [
        "print(y.shape)\n",
        "y = np.expand_dims(y, axis=0)\n",
        "print(y.shape)"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Y repetimos el contenido de `y` 32 veces a lo largo de ese eje de manera que pueden ser sumados por la función. Nótese que los datos realmente no se copian sino que a nivel algorítmico se simula que están repetidos 32 veces, pero esto nos ayuda mentalmente a programar algunas operaciones.  "
      ],
      "metadata": {
        "id": "ibpRXpstDRZ1"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-UcTxct8ugWC",
        "outputId": "1581fba5-b83c-4fd9-9065-84eaae2a57c2"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(32, 10)\n"
          ]
        }
      ],
      "source": [
        "Y = np.concatenate([y] * 32, axis=0)\n",
        "print(Y.shape)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(Y)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "r575eCJSkOs8",
        "outputId": "08225cb2-029f-4934-c688-09dcff365ffe"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.43480296 0.23893743 0.56142585 0.69313377 0.7801377  0.27820999\n",
            "  0.87437412 0.23970015 0.15495713 0.77891035]\n",
            " [0.43480296 0.23893743 0.56142585 0.69313377 0.7801377  0.27820999\n",
            "  0.87437412 0.23970015 0.15495713 0.77891035]\n",
            " [0.43480296 0.23893743 0.56142585 0.69313377 0.7801377  0.27820999\n",
            "  0.87437412 0.23970015 0.15495713 0.77891035]\n",
            " [0.43480296 0.23893743 0.56142585 0.69313377 0.7801377  0.27820999\n",
            "  0.87437412 0.23970015 0.15495713 0.77891035]\n",
            " [0.43480296 0.23893743 0.56142585 0.69313377 0.7801377  0.27820999\n",
            "  0.87437412 0.23970015 0.15495713 0.77891035]\n",
            " [0.43480296 0.23893743 0.56142585 0.69313377 0.7801377  0.27820999\n",
            "  0.87437412 0.23970015 0.15495713 0.77891035]\n",
            " [0.43480296 0.23893743 0.56142585 0.69313377 0.7801377  0.27820999\n",
            "  0.87437412 0.23970015 0.15495713 0.77891035]\n",
            " [0.43480296 0.23893743 0.56142585 0.69313377 0.7801377  0.27820999\n",
            "  0.87437412 0.23970015 0.15495713 0.77891035]\n",
            " [0.43480296 0.23893743 0.56142585 0.69313377 0.7801377  0.27820999\n",
            "  0.87437412 0.23970015 0.15495713 0.77891035]\n",
            " [0.43480296 0.23893743 0.56142585 0.69313377 0.7801377  0.27820999\n",
            "  0.87437412 0.23970015 0.15495713 0.77891035]\n",
            " [0.43480296 0.23893743 0.56142585 0.69313377 0.7801377  0.27820999\n",
            "  0.87437412 0.23970015 0.15495713 0.77891035]\n",
            " [0.43480296 0.23893743 0.56142585 0.69313377 0.7801377  0.27820999\n",
            "  0.87437412 0.23970015 0.15495713 0.77891035]\n",
            " [0.43480296 0.23893743 0.56142585 0.69313377 0.7801377  0.27820999\n",
            "  0.87437412 0.23970015 0.15495713 0.77891035]\n",
            " [0.43480296 0.23893743 0.56142585 0.69313377 0.7801377  0.27820999\n",
            "  0.87437412 0.23970015 0.15495713 0.77891035]\n",
            " [0.43480296 0.23893743 0.56142585 0.69313377 0.7801377  0.27820999\n",
            "  0.87437412 0.23970015 0.15495713 0.77891035]\n",
            " [0.43480296 0.23893743 0.56142585 0.69313377 0.7801377  0.27820999\n",
            "  0.87437412 0.23970015 0.15495713 0.77891035]\n",
            " [0.43480296 0.23893743 0.56142585 0.69313377 0.7801377  0.27820999\n",
            "  0.87437412 0.23970015 0.15495713 0.77891035]\n",
            " [0.43480296 0.23893743 0.56142585 0.69313377 0.7801377  0.27820999\n",
            "  0.87437412 0.23970015 0.15495713 0.77891035]\n",
            " [0.43480296 0.23893743 0.56142585 0.69313377 0.7801377  0.27820999\n",
            "  0.87437412 0.23970015 0.15495713 0.77891035]\n",
            " [0.43480296 0.23893743 0.56142585 0.69313377 0.7801377  0.27820999\n",
            "  0.87437412 0.23970015 0.15495713 0.77891035]\n",
            " [0.43480296 0.23893743 0.56142585 0.69313377 0.7801377  0.27820999\n",
            "  0.87437412 0.23970015 0.15495713 0.77891035]\n",
            " [0.43480296 0.23893743 0.56142585 0.69313377 0.7801377  0.27820999\n",
            "  0.87437412 0.23970015 0.15495713 0.77891035]\n",
            " [0.43480296 0.23893743 0.56142585 0.69313377 0.7801377  0.27820999\n",
            "  0.87437412 0.23970015 0.15495713 0.77891035]\n",
            " [0.43480296 0.23893743 0.56142585 0.69313377 0.7801377  0.27820999\n",
            "  0.87437412 0.23970015 0.15495713 0.77891035]\n",
            " [0.43480296 0.23893743 0.56142585 0.69313377 0.7801377  0.27820999\n",
            "  0.87437412 0.23970015 0.15495713 0.77891035]\n",
            " [0.43480296 0.23893743 0.56142585 0.69313377 0.7801377  0.27820999\n",
            "  0.87437412 0.23970015 0.15495713 0.77891035]\n",
            " [0.43480296 0.23893743 0.56142585 0.69313377 0.7801377  0.27820999\n",
            "  0.87437412 0.23970015 0.15495713 0.77891035]\n",
            " [0.43480296 0.23893743 0.56142585 0.69313377 0.7801377  0.27820999\n",
            "  0.87437412 0.23970015 0.15495713 0.77891035]\n",
            " [0.43480296 0.23893743 0.56142585 0.69313377 0.7801377  0.27820999\n",
            "  0.87437412 0.23970015 0.15495713 0.77891035]\n",
            " [0.43480296 0.23893743 0.56142585 0.69313377 0.7801377  0.27820999\n",
            "  0.87437412 0.23970015 0.15495713 0.77891035]\n",
            " [0.43480296 0.23893743 0.56142585 0.69313377 0.7801377  0.27820999\n",
            "  0.87437412 0.23970015 0.15495713 0.77891035]\n",
            " [0.43480296 0.23893743 0.56142585 0.69313377 0.7801377  0.27820999\n",
            "  0.87437412 0.23970015 0.15495713 0.77891035]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "gzMWYxsxugWC"
      },
      "outputs": [],
      "source": [
        "def naive_add_matrix_and_vector(x, y):\n",
        "    assert len(x.shape) == 2\n",
        "    assert len(y.shape) == 1\n",
        "    assert x.shape[1] == y.shape[0]\n",
        "    x = x.copy()\n",
        "    for i in range(x.shape[0]):\n",
        "        for j in range(x.shape[1]):\n",
        "            x[i, j] += y[j]\n",
        "    return x"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "9i9SFlqougWC"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "x = np.random.random((64, 3, 32, 10))\n",
        "y = np.random.random((32, 10))\n",
        "z = np.maximum(x, y)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Z9uN6Gh8ugWD"
      },
      "source": [
        "### Tensor product"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "rpFcEDs6ugWD"
      },
      "outputs": [],
      "source": [
        "x = np.random.random((32,))\n",
        "y = np.random.random((32,))\n",
        "z = np.dot(x, y)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "VLcjtU4GugWD"
      },
      "outputs": [],
      "source": [
        "def naive_vector_dot(x, y):\n",
        "    assert len(x.shape) == 1\n",
        "    assert len(y.shape) == 1\n",
        "    assert x.shape[0] == y.shape[0]\n",
        "    z = 0.\n",
        "    for i in range(x.shape[0]):\n",
        "        z += x[i] * y[i]\n",
        "    return z"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "EC5BYo7GugWE"
      },
      "outputs": [],
      "source": [
        "def naive_matrix_vector_dot(x, y):\n",
        "    assert len(x.shape) == 2\n",
        "    assert len(y.shape) == 1\n",
        "    assert x.shape[1] == y.shape[0]\n",
        "    z = np.zeros(x.shape[0])\n",
        "    for i in range(x.shape[0]):\n",
        "        for j in range(x.shape[1]):\n",
        "            z[i] += x[i, j] * y[j]\n",
        "    return z"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "aOJYvDrrugWE"
      },
      "outputs": [],
      "source": [
        "def naive_matrix_vector_dot(x, y):\n",
        "    z = np.zeros(x.shape[0])\n",
        "    for i in range(x.shape[0]):\n",
        "        z[i] = naive_vector_dot(x[i, :], y)\n",
        "    return z"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "DNzcAyivugWE"
      },
      "outputs": [],
      "source": [
        "def naive_matrix_dot(x, y):\n",
        "    assert len(x.shape) == 2\n",
        "    assert len(y.shape) == 2\n",
        "    assert x.shape[1] == y.shape[0]\n",
        "    z = np.zeros((x.shape[0], y.shape[1]))\n",
        "    for i in range(x.shape[0]):\n",
        "        for j in range(y.shape[1]):\n",
        "            row_x = x[i, :]\n",
        "            column_y = y[:, j]\n",
        "            z[i, j] = naive_vector_dot(row_x, column_y)\n",
        "    return z"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gZRngl6dugWF"
      },
      "source": [
        "### Tensor reshaping\n",
        "\n",
        "Reformar o reorganizar un tensor para que sus forma encaje con la de deseada. Esto lo hicimos al preprocesar MNIST:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "WY0IwUBrugWF"
      },
      "outputs": [],
      "source": [
        "train_images = train_images.reshape((60000, 28 * 28))"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Un ejemplo de reorganización de tensores sería: "
      ],
      "metadata": {
        "id": "hzZhYRctJzDY"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "yQivEezOugWF",
        "outputId": "47ea3041-a3d4-46a1-e480-937a5742e7b9"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(3, 2)"
            ]
          },
          "metadata": {},
          "execution_count": 67
        }
      ],
      "source": [
        "x = np.array([[0., 1.],\n",
        "             [2., 3.],\n",
        "             [4., 5.]])\n",
        "x.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zLCm38uqugWG",
        "outputId": "f3a39fbc-ef4a-47f4-8e0e-5dd3ae2f6683"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.],\n",
              "       [1.],\n",
              "       [2.],\n",
              "       [3.],\n",
              "       [4.],\n",
              "       [5.]])"
            ]
          },
          "metadata": {},
          "execution_count": 68
        }
      ],
      "source": [
        "x = x.reshape((6, 1))\n",
        "x"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Un ejemplo especial de reorganización sería la transposición que significa que una matriz intercambia sus filas y columnas de manera que `x[i, :]` se convierte en `x[:, i]:`"
      ],
      "metadata": {
        "id": "aCtZHWrWJ-ov"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "aYwaK2VGugWG",
        "outputId": "f283e3b5-54cb-41a4-ee46-faaa88f80959"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(20, 300)"
            ]
          },
          "metadata": {},
          "execution_count": 69
        }
      ],
      "source": [
        "x = np.zeros((300, 20))\n",
        "x = np.transpose(x)\n",
        "x.shape"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AKarzUb-ugWG"
      },
      "source": [
        "### Geometric interpretation of tensor operations"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OhJRM9lYugWG"
      },
      "source": [
        "### A geometric interpretation of deep learning"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2MDfXxEvugWG"
      },
      "source": [
        "## El motor de las redes neuronales: la optimización por gradiente"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jvLx0G-nugWH"
      },
      "source": [
        "### ¿Qué es una derivada?\n",
        "\n",
        "[Fuente Choller 2022]\n",
        "![imagen.png](data:image/png;base64,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)"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Derivadas y optimización:** cómo encontrar valores de `x` (multiplicados por un factor episilon) para minimizar `f(x)`. Conocida la derivada de `f` conocemos cómo evoluciona `f(x)` y por tanto mover `x` (en dirección opuesta a la derivada) para minimizarlo.\n",
        "\n"
      ],
      "metadata": {
        "id": "TcFXfl9_TZp7"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mCYaZwCyugWH"
      },
      "source": [
        "### Derivada de una operación con tensores: el gradiente\n",
        "\n",
        "El **gradiente** es la generalización del concepto de derivada a funciones que procesan tensores como entradas. Si para una función escalar la derivada representa la **pendiente** local de la función, el gradiente de una función de tensores representa la **curvatura** de la superficie multidimensional descrita por la función. Pero al final nos dice cómo cambia la salida de la función según varíen los parámetros de entrada. \n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "[Fuente Choller 2022] \n",
        "![imagen.png](data:image/png;base64,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)"
      ],
      "metadata": {
        "id": "iCxqlG3tWoko"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Un ejemplo en el contexto de aprendizaje máquina: \n",
        "* Vector de entrada `x` (muestra en el conjunto de datos)\n",
        "* Matriz `W` (los pesos del modelo que queremos ajustar)\n",
        "* Objetivo `y_true` (que el modelo debe aprender a asociar con `x`)\n",
        "* Función de pérdida `loss` (que mide la distancia entre las predicciones del modelo y `y_true`)\n",
        "\n",
        "\n",
        "```\n",
        "y_pred = dot(W, x)\n",
        "loss_value = loss(y_pred, y_true)\n",
        "```\n",
        "\n",
        "Como las entradas `x` y `y_true` podemos considerar que el valor que minimizamos depende sólo de `W`.\n",
        "\n",
        "\n",
        "```\n",
        "loss_value = f(W)\n",
        "```\n",
        "\n",
        "Si `W0` es un valor actual de `W`, la derivada de `f` en el punto `W0` es un tensor `grad(loss_value, W0)` con la misma forma que `W` donde cada coeficiente `grad(loss_value, W0)[i, j]` indica la dirección y magnitud del cambio en el coste que observamos al modificar `W0[i, j]`. Por tanto, el gradiente se puede descomponer varias funciones escalares que nos dan las **derivadas parciales** de la función de coste con respecto a cada parámetro de la red. \n",
        "\n"
      ],
      "metadata": {
        "id": "WcD_KejIdVa_"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "A3T1ljSxugWH"
      },
      "source": [
        "### Descenso por gradiente estocástico (SGD)\n",
        "\n",
        "Algoritmo general de **descenso por gradiente estocástico** (*stochastic gradient descent*, SGD)\n",
        "1. Extraer un lote (*batch*) de patrones de entrenamiento, `x` y sus etiquetas `y_true`\n",
        "1. Usar el modelo para obtener las predicciones, `y_pred` (*forward pass*)\n",
        "1. Calcular el coste del modelo (discrepancia `y_pred` e `y_true`) para el lote de patrones.\n",
        "1. Calcular el gradiente de la función de coste respecto a los parámetros del modelo (*backward pass*).\n",
        "1. Cambiar los parámetros un poco en la dirección opuesta al gradiente (ej. `W -= learning_rate * gradient`) para reducir el coste un poco. El factor de aprendizaje o learning rate es un número que modula la 'velocidad' del descenso por gradiente. \n",
        "\n",
        "[Fuente Chollet 2022]\n",
        "![imagen.png](data:image/png;base64,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)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        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)"
      ],
      "metadata": {
        "id": "n0fRQROHg0sg"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "\n",
        "```\n",
        "past_velocity = 0. \n",
        "momentum = 0.1\n",
        "while loss > 0.01:\n",
        "    w, loss, gradient = get_current_parameters()\n",
        "    velocity = past_velocity * momentum - learning_rate * gradient\n",
        "    w = w + momentum * velocity - learning_rate * gradient\n",
        "    past_velocity = velocity\n",
        "    update_parameter(w)\n",
        "```\n",
        "\n"
      ],
      "metadata": {
        "id": "qEpbMHQrg6HX"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Ver [optimizadores disponibles en Keras](https://keras.io/api/optimizers/#available-optimizers)."
      ],
      "metadata": {
        "id": "2KOCvpQThmhJ"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xdM2uClUugWI"
      },
      "source": [
        "### Algoritmo de retropropagación"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "q22txNCyugWI"
      },
      "source": [
        "#### La regla de la cadena"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Nuestro modelo totalmente conectado: "
      ],
      "metadata": {
        "id": "ATHhFbXzj4fc"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from tensorflow import keras \n",
        "from tensorflow.keras import layers\n",
        "model = keras.Sequential([\n",
        "    layers.Dense(512, activation=\"relu\"),\n",
        "    layers.Dense(10, activation=\"softmax\")\n",
        "])"
      ],
      "metadata": {
        "id": "JblPLhc6jJ78"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Se puede descomponer en una serie de operaciones simples con derivadas directas mediante la *regla de la cadena*: \n",
        "\n",
        "\n",
        "```\n",
        "loss_value = loss(y_true, softmax(dot(relu(dot(inputs, W1) + b1), W2) + b2))\n",
        "```\n",
        "\n"
      ],
      "metadata": {
        "id": "kGhhxBSNjaTU"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mJmosdjTugWI"
      },
      "source": [
        "#### Grafos de computación y derivación automática "
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Los **grafos de computación** son una forma de expresar explícitamente la arquitectura de los modelos de aprendizaje profundo de manera que puedan ser procesables por funciones. \n",
        "\n",
        "Este es el grafo de computación de nuestro modelo.\n",
        "\n",
        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)"
      ],
      "metadata": {
        "id": "3k0_Xy7nkGY0"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "❓❓❓**Ejercicio grafo computación**:❓❓❓ realizar una ejecución del algoritmo de retropropagación sobre este grafo de computación. Valores de entradas y parámetros: `x=2`, `w=3`, `b=1`, `y_true=4`\n",
        "\n",
        "![imagen.png](data:image/png;base64,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)"
      ],
      "metadata": {
        "id": "4u_eQXZwpFFJ"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZbB6Tp8-ugWJ"
      },
      "source": [
        "#### Diferenciación automática (gradient tape en TensorFlow)\n",
        "\n",
        "Hoy en día la gente implementa redes neuronales con herramientas modernas que son capaces de diferenciar automáticamente, como TensorFlow. La diferenciación automática se implementa con el tipo de grafo de computación que acabamos de ver. La diferenciación automática permite calcular los gradientes de composiciones arbitrarias de operaciones con tensores diferenciables sin hacer nada más que escribir el pase hacia delante (*forward pass*).\n",
        "\n",
        "TensorFlow implementa la diferenciación automática a través del API `GradientTape`. `GradientTape` permite obtener el gradiente de cualquier salida con respecto a cualquier variable o conjunto de variables (ej. `tf.Variable`)."
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Evaluar el gradiente de la función ` y = 2 * x + 3` en el punto `x = 0.0`"
      ],
      "metadata": {
        "id": "LbUXC7slFMMC"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ghEGbm3QugWJ"
      },
      "outputs": [],
      "source": [
        "import tensorflow as tf\n",
        "x = tf.Variable(0.)\n",
        "with tf.GradientTape() as tape:\n",
        "    y = 2 * x + 3\n",
        "grad_of_y_wrt_x = tape.gradient(y, x)\n",
        "print(grad_of_y_wrt_x)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Y8Hvpq9-ugWJ"
      },
      "outputs": [],
      "source": [
        "x = tf.Variable(tf.random.uniform((2, 2)))\n",
        "with tf.GradientTape() as tape:\n",
        "    y = 2 * x + 3\n",
        "grad_of_y_wrt_x = tape.gradient(y, x)\n",
        "print(grad_of_y_wrt_x)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "3vureaTxugWK"
      },
      "outputs": [],
      "source": [
        "W = tf.Variable(tf.random.uniform((2, 2)))\n",
        "b = tf.Variable(tf.zeros((2,)))\n",
        "x = tf.random.uniform((2, 2))\n",
        "with tf.GradientTape() as tape:\n",
        "    y = tf.matmul(x, W) + b # matmul igual a dot en numpy\n",
        "grad_of_y_wrt_W_and_b = tape.gradient(y, [W, b])\n",
        "print(grad_of_y_wrt_x)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Cmjg7jWvugWK"
      },
      "source": [
        "## Vuelta al modelo de ejemplo inicial\n",
        "\n",
        "Después de las secciones anteriores tenemos una idea general de qué hay detrás de las redes neuronales profundas.\n",
        "\n",
        "Relaciones entre capas de la red, función de pérdida y optimizador. \n",
        "\n",
        "![imagen.png](data:image/png;base64,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)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Revisitemos el ejemplo inicial. \n",
        "\n",
        "Estos eran los datos de entrada.\n",
        "\n",
        "❓❓❓¿Cómo se almacenan las imágenes de los datos de entrenamiento y test? ❓❓❓"
      ],
      "metadata": {
        "id": "L7N6mdcrIHb2"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "yMmmQ8cKugWL"
      },
      "outputs": [],
      "source": [
        "(train_images, train_labels), (test_images, test_labels) = mnist.load_data()\n",
        "train_images = train_images.reshape((60000, 28 * 28))\n",
        "train_images = train_images.astype(\"float32\") / 255\n",
        "test_images = test_images.reshape((10000, 28 * 28))\n",
        "test_images = test_images.astype(\"float32\") / 255"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Nuestro modelo está compuesto de una cadena de dos capas `Dense` y que cada una aplica unas operaciones simples a los datos de entrada, y que estas operaciones implican tensores de pesos. "
      ],
      "metadata": {
        "id": "R0yMEu60IduJ"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "GNepUXnZugWN"
      },
      "outputs": [],
      "source": [
        "model = keras.Sequential([\n",
        "    layers.Dense(512, activation=\"relu\"),\n",
        "    layers.Dense(10, activation=\"softmax\")\n",
        "])"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Compilación del modelo. Ahora podemos entender que `sparse_categorical_crossentropy` es la función de pérdida que se usa como señal de feedback para el aprendizaje del los tensores de pesos y que el algoritmo de aprendizaje intentará minimizar. "
      ],
      "metadata": {
        "id": "XSDo4UmzJR2U"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Tnbkmp4BugWN"
      },
      "outputs": [],
      "source": [
        "model.compile(optimizer=\"rmsprop\",\n",
        "              loss=\"sparse_categorical_crossentropy\",\n",
        "              metrics=[\"accuracy\"])"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Finalmente, el bucle de entrenamiento. \n",
        "❓❓❓¿qué significa `epoch`?¿Qué pasará al ejecutar fit con estos parámetros?¿cuántas actualizaciones del gradiente se producirán con este conjunto de entrenamiento❓❓❓"
      ],
      "metadata": {
        "id": "oXRqxeRLKsnf"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "VkmBfa6pugWO"
      },
      "outputs": [],
      "source": [
        "model.fit(train_images, train_labels, epochs=5, batch_size=128)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vZPUYr1xugWP"
      },
      "source": [
        "### Reimplementando nuestro ejemplo desde cero en TensorFlow"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6Rad4u8KugWP"
      },
      "source": [
        "#### Clase Dense\n",
        "\n",
        "La clase `Dense` implementa la siguiente transformación de los datos de entrada donde `W` y `b` son los datos del modelo:\n",
        "\n",
        "```\n",
        "output = activation(dot(W, input) + b)\n",
        "```\n",
        "\n",
        "Donde la función de actividad suele ser `relu` para capas ocultas o `softmax` en la última capa.\n",
        "\n",
        "Nota de orientación a objetos en Python: \n",
        "* El método `__init__` es el constructor de la clase y se llama al crear una instancia de la clase para asignar valores por defecto a los atributos de la clase. \n",
        "* El método `__call__` es el método que se lanza cuando se llama a la instancia de la clase como si fuera una función. \n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "wGqA3sy3ugWP"
      },
      "outputs": [],
      "source": [
        "import tensorflow as tf\n",
        "\n",
        "class NaiveDense:\n",
        "    def __init__(self, input_size, output_size, activation):\n",
        "        self.activation = activation\n",
        "\n",
        "        w_shape = (input_size, output_size)\n",
        "        w_initial_value = tf.random.uniform(w_shape, minval=0, maxval=1e-1)\n",
        "        self.W = tf.Variable(w_initial_value)\n",
        "\n",
        "        b_shape = (output_size,)\n",
        "        b_initial_value = tf.zeros(b_shape)\n",
        "        self.b = tf.Variable(b_initial_value)\n",
        "\n",
        "    def __call__(self, inputs):\n",
        "        return self.activation(tf.matmul(inputs, self.W) + self.b)\n",
        "\n",
        "    @property\n",
        "    def weights(self):\n",
        "        return [self.W, self.b]"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "❓❓❓ Intenta cambiar la forma de inicialización de los pesos y observa el efecto. ❓❓❓"
      ],
      "metadata": {
        "id": "hsE9tTRssFKp"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bX0Aiyr3ugWQ"
      },
      "source": [
        "#### Clase Sequential\n",
        "\n",
        "Esta clase se va a encargar de encadenar las capas. Va a empaquetar una lista de capas y expone un método `__call__()` que simplemente llama en orden a las capas subyacentes. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "jfso4YniugWQ"
      },
      "outputs": [],
      "source": [
        "class NaiveSequential:\n",
        "    def __init__(self, layers):\n",
        "        self.layers = layers\n",
        "\n",
        "    def __call__(self, inputs):\n",
        "        x = inputs\n",
        "        for layer in self.layers:\n",
        "           x = layer(x)\n",
        "        return x\n",
        "\n",
        "    @property\n",
        "    def weights(self):\n",
        "       weights = []\n",
        "       for layer in self.layers:\n",
        "           weights += layer.weights\n",
        "       return weights"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Usando las clases `NaiveDense` y `NaiveSequential` podemos crear algo similar a un modelo de Keras:"
      ],
      "metadata": {
        "id": "j81P9OhoQetU"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "qOIdPFPbugWQ"
      },
      "outputs": [],
      "source": [
        "model = NaiveSequential([\n",
        "    NaiveDense(input_size=28 * 28, output_size=512, activation=tf.nn.relu),\n",
        "    NaiveDense(input_size=512, output_size=10, activation=tf.nn.softmax)\n",
        "])\n",
        "assert len(model.weights) == 4"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "❓❓❓Prueba a cambiar: la función de activación de la capa oculta, el tamaño de salida, etc.❓❓❓"
      ],
      "metadata": {
        "id": "zF3wrbTcQs3h"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ek_YvseeugWR"
      },
      "source": [
        "#### Generador de lotes o *batches* \n",
        "\n",
        "Esta clase nos permitirá iterar sobre las imágenes de entrenamiento en *mini-batches*."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "nVUExC7hugWR"
      },
      "outputs": [],
      "source": [
        "import math\n",
        "\n",
        "class BatchGenerator:\n",
        "    def __init__(self, images, labels, batch_size=128):\n",
        "        assert len(images) == len(labels)\n",
        "        self.index = 0\n",
        "        self.images = images\n",
        "        self.labels = labels\n",
        "        self.batch_size = batch_size\n",
        "        self.num_batches = math.ceil(len(images) / batch_size)\n",
        "\n",
        "    def next(self):\n",
        "        images = self.images[self.index : self.index + self.batch_size]\n",
        "        labels = self.labels[self.index : self.index + self.batch_size]\n",
        "        self.index += self.batch_size\n",
        "        return images, labels"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7PXxSP3SugWR"
      },
      "source": [
        "### Ejecutar un paso de entrenamiento\n",
        "\n",
        "La parte más difícil del proceso es el \"paso de entrenamiento\": actualizar los pesos del modelo después de procesar un lote de datos. Necesitamos: \n",
        "1. Calcular las predicciones del modelo para las imágenes del lote.\n",
        "1. Calcular el valor de la pérdida para estas predicciones, dadas las etiquetas reales.\n",
        "1. Calcular el gradiente de la pérdida con respecto a los pesos del modelo.\n",
        "1. Mover los pesos una pequeña cantidad en la dirección opuesta al gradiente. \n",
        "\n",
        "El gradiente lo vamos a calcular con `GradientTape` de TensorFlow."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "WW-YoylIugWR"
      },
      "outputs": [],
      "source": [
        "def one_training_step(model, images_batch, labels_batch):\n",
        "    with tf.GradientTape() as tape:\n",
        "        predictions = model(images_batch) # llama a __call__()\n",
        "        per_sample_losses = tf.keras.losses.sparse_categorical_crossentropy(\n",
        "            labels_batch, predictions)\n",
        "        # media de elementos a través de las dimensiones del tensor\n",
        "        average_loss = tf.reduce_mean(per_sample_losses)\n",
        "    # gradiente del la función de coste/pérdida respecto a los pesos del modelo\n",
        "    # de todas las capas\n",
        "    gradients = tape.gradient(average_loss, model.weights)\n",
        "    update_weights(gradients, model.weights)\n",
        "    return average_loss"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "La función `update_weights` moverá los pesos \"un poco\" en la dirección que reduzca la pérdida para este lote. La magnitud de este movimiento dependerá del `learning_rate` y será en dirección contaria al gradiente, por tanto basta con restar el gradiente multiplicado por `learning_rate` a los pesos para actualizarlos. \n",
        "\n",
        "Nota Python: [cómo funciona zip](https://www.freecodecamp.org/news/the-zip-function-in-python-explained-with-examples/)."
      ],
      "metadata": {
        "id": "3gB5qSZ0VK-I"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "b4rVo3mgugWR"
      },
      "outputs": [],
      "source": [
        "learning_rate = 1e-3\n",
        "\n",
        "def update_weights(gradients, weights):\n",
        "    for g, w in zip(gradients, weights):\n",
        "        w.assign_sub(g * learning_rate)"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "En la práctica será muy raro que implementemos la actualización de los pesos a mano y utilizaremos uno de los optimizadores de Keras:"
      ],
      "metadata": {
        "id": "H6V-aZ5AWtrx"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "BlEYGwT3ugWS"
      },
      "outputs": [],
      "source": [
        "from tensorflow.keras import optimizers\n",
        "\n",
        "optimizer = optimizers.SGD(learning_rate=1e-3)\n",
        "\n",
        "def update_weights(gradients, weights):\n",
        "    optimizer.apply_gradients(zip(gradients, weights))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iEx1Hih-ugWS"
      },
      "source": [
        "### El bucle de aprendizaje completo\n",
        "\n",
        "Una época o *epoch* de aprendizaje consiste en repetir un paso de aprendizaje para cada lote del conjunto de entrenamiento. El bucle completo de aprendizaje es simplemente la repetición de una época. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "XrL_f9piugWS"
      },
      "outputs": [],
      "source": [
        "def fit(model, images, labels, epochs, batch_size=128):\n",
        "    loss_history = list()\n",
        "    for epoch_counter in range(epochs):\n",
        "        print(f\"Epoch {epoch_counter}\")\n",
        "        batch_generator = BatchGenerator(images, labels)\n",
        "        for batch_counter in range(batch_generator.num_batches):\n",
        "            images_batch, labels_batch = batch_generator.next()\n",
        "            loss = one_training_step(model, images_batch, labels_batch)\n",
        "            loss_history.append(loss.numpy())\n",
        "            if batch_counter % 100 == 0:\n",
        "                print(f\"loss at batch {batch_counter}: {loss:.2f}\")\n",
        "    return model, loss_history"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Probemos nuestro modelo: "
      ],
      "metadata": {
        "id": "7ItBUzzUZ2gy"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "oL2E5EEHugWS",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d9fa21e0-6d80-4d98-c5a5-0240687868e7"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 0\n",
            "loss at batch 0: 14.86\n",
            "loss at batch 100: 13.85\n",
            "loss at batch 200: 14.36\n",
            "loss at batch 300: 14.61\n",
            "loss at batch 400: 14.61\n",
            "Epoch 1\n",
            "loss at batch 0: 14.86\n",
            "loss at batch 100: 13.85\n",
            "loss at batch 200: 14.36\n",
            "loss at batch 300: 14.61\n",
            "loss at batch 400: 14.61\n"
          ]
        }
      ],
      "source": [
        "from tensorflow.keras.datasets import mnist\n",
        "(train_images, train_labels), (test_images, test_labels) = mnist.load_data()\n",
        "\n",
        "train_images = train_images.reshape((60000, 28 * 28))\n",
        "train_images = train_images.astype(\"float32\") / 255\n",
        "test_images = test_images.reshape((10000, 28 * 28))\n",
        "test_images = test_images.astype(\"float32\") / 255\n",
        "\n",
        "mode, loss_history = fit(model, train_images, train_labels, epochs=10, batch_size=128)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "plt.plot(loss_history)\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "iVuCpObGcUhe",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "249dfd45-9e8d-4e6c-ac09-5660962f9abd"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "❓❓❓ Analiza la salida de la evolución de la función de error. ¿Ha sido siempre descendente?\n",
        "\n",
        "¿Qué podríamos hacer para mejorar la precisión?\n",
        "\n",
        "Prueba a reemplazar el optimizador por [otro de Keras](https://keras.io/api/optimizers/).\n",
        "\n",
        "Prueba a cambiar la tasa de aprendizaje y a activar el momento.❓❓❓"
      ],
      "metadata": {
        "id": "KmOcXEE8XhbV"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "knkPRk_-ugWT"
      },
      "source": [
        "### Evaluación del modelo\n",
        "\n",
        "Podemos evaluar el modelo eligiendo la neurona de salida con máximo valor en la predicción del conjunto de test y comparándola con la etiqueta esperada:\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "D65ho0WiugWT",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "1dcbbe7e-11c3-4882-8434-cdcd2032bafe"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "accuracy: 0.81\n"
          ]
        }
      ],
      "source": [
        "import numpy as np\n",
        "predictions = model(test_images)\n",
        "predictions = predictions.numpy()\n",
        "predicted_labels = np.argmax(predictions, axis=1)\n",
        "matches = predicted_labels == test_labels\n",
        "print(f\"accuracy: {matches.mean():.2f}\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_fzjUItJugWT"
      },
      "source": [
        "## Resumen"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "* Los *tensores* constituyen las bases de los métodos de aprendizaje máquina modernos. \n",
        "* Los tensores numéricos se pueden manipular a través de *operaciones de tensores* (suma, producto, multiplicación elemento a elemento...).\n",
        "* Los modelos de aprendizaje profundo consisten en una cadena de operaciones de tensores sencillas parametrizadas por los *pesos*, que también son tensores. Los pesos de un modelo es donde se recoge el \"conocimiento\" del problema. \n",
        "* En este contexto, *aprender* significa encontrar un conjunto de valores para los pesos del modelo que minimizan una *función de pérdida* para un conjunto de patrones de entrenamiento y sus etiquetas. \n",
        "* Descenso por gradiente estocástico con mini-lotes (mini-batch stochastic gradient descent). \n",
        "* El proceso de aprendizaje es posible porque todas las operaciones de tensores en las redes son diferenciables. \n",
        "* Conceptos clave: pérdida o *loss* y optimizadores. \n"
      ],
      "metadata": {
        "id": "DmpSN_bbfGQo"
      }
    }
  ],
  "metadata": {
    "colab": {
      "collapsed_sections": [],
      "name": "chapter02_mathematical-building-blocks-network-from-scratch.ipynb",
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.7.0"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}