Python_para_ML_03.ipynb

{
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  "metadata": {
    "colab": {
      "name": "Python para ML - 03.ipynb",
      "provenance": [],
      "authorship_tag": "ABX9TyOw7aMSGiMDMeCyHBkzWGqJ",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/ricardorocha86/Python-para-Machine-Learning/blob/master/Python_para_ML_03.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "y-tWWWUKwsQ8",
        "colab_type": "text"
      },
      "source": [
        "![alt text](https://raw.githubusercontent.com/ricardorocha86/Python-para-Machine-Learning/master/Imagens/capa%20-%20python%20para%20ml%2003.jpg)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "06dgfAJmv4fu",
        "colab_type": "text"
      },
      "source": [
        "# **Python para Machine Learning** - Parte 03"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_7pc3VLbxNNV",
        "colab_type": "text"
      },
      "source": [
        "Nesse notebook veremos:\n",
        "- Tuplas\n",
        "- Conjuntos\n",
        "- A Biblioteca Numpy\n",
        "- Projeto: simulação de um álbum de figurinhas\n",
        "- Exercícios\n",
        "- Links Úteis"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1l2tpVyWWB84",
        "colab_type": "text"
      },
      "source": [
        "## **Tuplas**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Hq1QGJGsYAPi",
        "colab_type": "text"
      },
      "source": [
        "Tuplas são muito similares a listas. São definidas utilizando parênteses **( )**. A diferença entre listas e tuplas é que tuplas não são mutáveis, isto é, você não consegue alterar o valor de uma entrada de uma tupla. Veja no exemplo."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zeEQcg15R-z-",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 36
        },
        "outputId": "6e5323d9-4ed0-46b3-fe7c-a39341f1d1df"
      },
      "source": [
        "lista = ['Ricardo', 33, True, len]\n",
        "tupla = ('Ricardo', 33, True, len)\n",
        "print(tupla[0])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Ricardo\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WwD6lwEfSJut",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 173
        },
        "outputId": "d6b6d03a-949b-42d7-8043-0bddb0fcc8c1"
      },
      "source": [
        "tupla[0] = 'Python'"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "error",
          "ename": "TypeError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-3-f89789468150>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mtupla\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m'Python'\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
            "\u001b[0;31mTypeError\u001b[0m: 'tuple' object does not support item assignment"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "R1BffMF2SFS_",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 36
        },
        "outputId": "67906975-d6a1-457c-d4c9-4d7e3448d2e4"
      },
      "source": [
        "lista[0] = 'Python'\n",
        "print(lista)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "['Python', 33, True, <built-in function len>]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nJlZkE7MYBEL",
        "colab_type": "text"
      },
      "source": [
        "Tuplas, em geral, são mais rápidas de se processar do que listas. Elas previnem que uma informação seja alterada ou modificada sem intenção. Elas não possuem o método **append** ou **extend**. No entanto, ela não são tão frequentemente utilizadas como são as listas. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9XQ9g5cPTK3Q",
        "colab_type": "text"
      },
      "source": [
        "## **Conjuntos**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vOwQDFd3TLBu",
        "colab_type": "text"
      },
      "source": [
        "Conjuntos é também um objeto básico do Python que simula um conjunto matemático. Neles, podemos armazenar elementos que não serão indexados e não permite repetições. Conjuntos são criados através da função **set** em uma lista ou utilizando **chaves { }**. Veja o exemplo."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ort4fxkmTrmE",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "conjunto1 = set(['carne', 'linguiça', 'frango', 'cerveja', 'refrigerante', 'carne', 'frango'])\n",
        "conjunto2 = {'carne', 'linguiça', 'frango', 'cerveja', 'refrigerante', 'carne', 'linguiça'}"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9gEVTn9CUDR-",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 73
        },
        "outputId": "78be44c3-cb95-45bb-d80a-52b64ff8b2fb"
      },
      "source": [
        "print(conjunto1)\n",
        "print(conjunto2)\n",
        "print(conjunto1 == conjunto2)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "{'carne', 'linguiça', 'refrigerante', 'frango', 'cerveja'}\n",
            "{'carne', 'linguiça', 'refrigerante', 'frango', 'cerveja'}\n",
            "True\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1nEIxFSYUzWx",
        "colab_type": "text"
      },
      "source": [
        "Alguns métodos importantes em conjuntos são as possíveis operações "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "F1GndKzvUAbf",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 202
        },
        "outputId": "4cc61b13-7733-48a0-f719-0d388b6d784c"
      },
      "source": [
        "conj1 = {'A', 'B', 'C', 1, 2, 3}\n",
        "conj2 = {'C', 'D', 'E', 3, 4, 5}\n",
        "print(conj1)\n",
        "print(conj2)\n",
        "\n",
        "print('\\nInterseção: ', conj1.intersection(conj2))\n",
        "print('\\nUnião: ', conj1.union(conj2))\n",
        "print('\\nSão disjuntos?: ', conj1.isdisjoint(conj2))\n",
        "print('\\nDiferença Simétrica: ', conj1.symmetric_difference(conj2))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "{'B', 1, 2, 3, 'A', 'C'}\n",
            "{3, 'E', 4, 5, 'D', 'C'}\n",
            "\n",
            "Interseção:  {3, 'C'}\n",
            "\n",
            "União:  {'B', 1, 2, 3, 'E', 'A', 4, 5, 'D', 'C'}\n",
            "\n",
            "São disjuntos?:  False\n",
            "\n",
            "Diferença Simétrica:  {'B', 1, 2, 4, 5, 'E', 'A', 'D'}\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "d4qDl7aWXlnN"
      },
      "source": [
        "## **A Biblioteca Numpy**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wBb8VajVYDEb",
        "colab_type": "text"
      },
      "source": [
        "Numpy é a biblioteca mais popular do python para se trabalhar com arrays. \n",
        "\n",
        "Arrays são conjuntos de valores, que podem ser n-dimensionais. \n",
        "\n",
        "Geralmente, um número apenas, um ponto, é um array de dimensão 0\n",
        "\n",
        "Uma lista de valores é um array de dimensão 1. \n",
        "\n",
        "Uma matriz de valores é uma array de dimensão 2. \n",
        "\n",
        "Um tensor de valores é um array de dimensão 3. \n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nvdq1LlPZXKH",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "64NE6_M6ZYxh",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "a0 = np.array(1)\n",
        "a1 = np.array([1, 2])\n",
        "a2 = np.array([[1, 2], [3, 4]])\n",
        "a3 = np.array([[[1, 2], [3, 4]], [[5, 6], [7, 8]]])"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0YWoD5e6aVwu",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 258
        },
        "outputId": "93511906-d017-4028-8d90-196e784b2fbd"
      },
      "source": [
        "print('Array a0:\\n', a0)\n",
        "print('Array a1:\\n', a1)\n",
        "print('Array a2:\\n', a2)\n",
        "print('Array a3:\\n', a3)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Array a0:\n",
            " 1\n",
            "Array a1:\n",
            " [1 2]\n",
            "Array a2:\n",
            " [[1 2]\n",
            " [3 4]]\n",
            "Array a3:\n",
            " [[[1 2]\n",
            "  [3 4]]\n",
            "\n",
            " [[5 6]\n",
            "  [7 8]]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zYn8Dx86Zcpw",
        "colab_type": "text"
      },
      "source": [
        "Use o atributo ndim para verificar a dimensão dos arrays numpy"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gGQQ1uQBZaLe",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 91
        },
        "outputId": "0231212e-1bed-4d56-be04-bb8a8a89ff44"
      },
      "source": [
        "print('Dimensão de a0:', a0.ndim)\n",
        "print('Dimensão de a1:', a1.ndim)\n",
        "print('Dimensão de a2:', a2.ndim)\n",
        "print('Dimensão de a3:', a3.ndim)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Dimensão de a0: 0\n",
            "Dimensão de a1: 1\n",
            "Dimensão de a2: 2\n",
            "Dimensão de a3: 3\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kXGd2r3ra0X9",
        "colab_type": "text"
      },
      "source": [
        "Transforme uma lista em um array"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "497CDTd9awol",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "lista = [1, 2, 3, 4]\n",
        "array = np.array(lista)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "u6PBFagAa7VP",
        "colab_type": "text"
      },
      "source": [
        "Arrays são feitos para se trabalhar com álgebra linear. Veja a diferença quando multiplicamos cada elemento por um escalar"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KbhXL49ibF50",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        },
        "outputId": "d50caf94-d885-4d84-a47a-766c9a4d9d35"
      },
      "source": [
        "print(2*lista)\n",
        "print(2*array)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[1, 2, 3, 4, 1, 2, 3, 4]\n",
            "[2 4 6 8]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "g7VxSD9DbJYl",
        "colab_type": "text"
      },
      "source": [
        "Similarmente, podemos realizar as demais operações com arrays"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DRPNPtIibP3s",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 128
        },
        "outputId": "2fc14ccd-e3f2-4438-d001-b5a86bc77fcd"
      },
      "source": [
        "print(array + array)\n",
        "print(array * 2)\n",
        "print(array / 3)\n",
        "print(array ** 2)\n",
        "print(array // 2)\n",
        "print(array % 2)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[2 4 6 8]\n",
            "[2 4 6 8]\n",
            "[0.33333333 0.66666667 1.         1.33333333]\n",
            "[ 1  4  9 16]\n",
            "[0 1 1 2]\n",
            "[1 0 1 0]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HA-R9IXDeaj4",
        "colab_type": "text"
      },
      "source": [
        "Algumas funções úteis do numpy"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IHtGwtxoeQO3",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        },
        "outputId": "e5f1c489-96ca-4850-bdcc-0623ad0bd62e"
      },
      "source": [
        "matriz = np.array([[1, 3], [4, 6]])\n",
        "print(matriz)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[1 3]\n",
            " [4 6]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zz6fottjfOWD",
        "colab_type": "text"
      },
      "source": [
        "Determinante de uma matriz"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bdyEcQHjfOeC",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from numpy.linalg import det"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "607fb4JcfUQe",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 36
        },
        "outputId": "f6a6ccab-1ae4-4a00-e212-b17d86f2f3a3"
      },
      "source": [
        "det(matriz)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "-6.0"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 72
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zT0U-14jfBA5",
        "colab_type": "text"
      },
      "source": [
        "Inversa de matriz"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IeC6D5z_bSqu",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from numpy.linalg import inv"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3sYA1uiofgqW",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        },
        "outputId": "c0207ea7-6b31-4c32-d1b5-dcbbc6d03ab6"
      },
      "source": [
        "inv(matriz)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-1.        ,  0.5       ],\n",
              "       [ 0.66666667, -0.16666667]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 74
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xbR8QbKVfgyZ",
        "colab_type": "text"
      },
      "source": [
        "Produto de matrizes"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "q4fQoAapekFF",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        },
        "outputId": "b965d631-ec82-41f1-b8c8-cb0439552dc8"
      },
      "source": [
        "np.dot(inv(matriz), matriz)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1., 0.],\n",
              "       [0., 1.]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 73
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HDbdEyppgNn-",
        "colab_type": "text"
      },
      "source": [
        "Gerar sequência de valores"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "of72OMEKgRql",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 36
        },
        "outputId": "779555c0-a4ae-47ba-89b2-8aeb766a87ce"
      },
      "source": [
        "seq = np.arange(1, 4.1, .2)\n",
        "print(seq)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[1.  1.2 1.4 1.6 1.8 2.  2.2 2.4 2.6 2.8 3.  3.2 3.4 3.6 3.8 4. ]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MJQ3r308g3Cx",
        "colab_type": "text"
      },
      "source": [
        "O atributo **shape** retorna a quantidade de valores no array"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nsOo-5VoglLk",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 36
        },
        "outputId": "2218fbcc-848f-4fbc-accf-d8fe6b8a04b1"
      },
      "source": [
        "seq.shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(16,)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 89
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mcg4xQrig9kt",
        "colab_type": "text"
      },
      "source": [
        "O método **reshape** permite alterar a distribuição de um array, mudando sua dimensão"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fFmaPVxlgN3i",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 91
        },
        "outputId": "ae3df79e-a3e8-4343-b2e4-490f1e147dfc"
      },
      "source": [
        "seq.reshape(4,4)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1. , 1.2, 1.4, 1.6],\n",
              "       [1.8, 2. , 2.2, 2.4],\n",
              "       [2.6, 2.8, 3. , 3.2],\n",
              "       [3.4, 3.6, 3.8, 4. ]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 90
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bTgFCTLvhGQ4",
        "colab_type": "text"
      },
      "source": [
        "O numpy possui uma sub-biblioteca para geração de números aleatórios"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GbN300J_hM5G",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 128
        },
        "outputId": "7245007e-dc53-4216-ae47-bcbf185cbf86"
      },
      "source": [
        "rnorms = np.random.normal(loc = 4, scale = 2, size = 12) #para gerar 12 valores de uma N(0,4)\n",
        "print(rnorms)\n",
        "\n",
        "mnorms = rnorms.reshape(3,4) #para gerar uma matriz de valores normais 3 linhas 4 colunas\n",
        "print(mnorms)\n",
        "print(mnorms.shape)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[ 6.14348357  5.45778013  2.14119727  3.69347171  4.96969273 -0.36854449\n",
            "  1.99447767  7.31343035  5.5009071   4.3051148   2.32623533  0.46481024]\n",
            "[[ 6.14348357  5.45778013  2.14119727  3.69347171]\n",
            " [ 4.96969273 -0.36854449  1.99447767  7.31343035]\n",
            " [ 5.5009071   4.3051148   2.32623533  0.46481024]]\n",
            "(3, 4)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aIoiDYRvfs4V",
        "colab_type": "text"
      },
      "source": [
        "Ajuste de um polinômio de grau ``n``"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nwUphutqYDOI",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 36
        },
        "outputId": "f6b789e1-77e3-4397-f00c-6ddfa3e76b21"
      },
      "source": [
        "x = [1, 2, 3, 4, 5]\n",
        "y = [3, 5, 7, 9, 11] # exatamente 2x + 1\n",
        "\n",
        "np.polyfit(x, y, deg = 1) #retorna b1 e b0, como na equacao b1*x + b0"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([2., 1.])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 75
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "igTLyL1r0IqK",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 300
        },
        "outputId": "ff3b5616-10f9-453c-be83-8d507d89467c"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "x = np.random.uniform(low = 1, high = 10, size = 100)\n",
        "y = 2*x + 1 + np.random.normal(0, 1, len(x))\n",
        "\n",
        "b1, b0 = np.polyfit(x, y, deg = 1)\n",
        "\n",
        "plt.figure(figsize=(8,4))\n",
        "plt.plot(x, y, '.', marker = '^', alpha = 0.4) #scatter plot dos pontos\n",
        "plt.plot(x, b0 + b1*x, color = 'green', alpha = 0.5) #plot da reta de regressão\n",
        "plt.title('Regressão Linear')\n",
        "plt.show() #comando para o output ficar um pouco melhor\n",
        "\n",
        "print(b1, b0)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 576x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "1.9971159210684446 0.992220996321161\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sdcEbegM1p7V",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 300
        },
        "outputId": "469f286b-9a2a-4086-ab9b-593f9cb8ca10"
      },
      "source": [
        "x = np.random.uniform(low = 1, high = 10, size = 500)\n",
        "y = x**2 - 8*x + +50 + np.random.normal(0, 3, len(x))\n",
        "\n",
        "b1, b0 = np.polyfit(x, y, deg = 1)\n",
        "\n",
        "c2, c1, c0 = np.polyfit(x, y, deg = 2)\n",
        "\n",
        "ex = np.arange(1, 10, 0.05)\n",
        "\n",
        "plt.title('Comparações')\n",
        "plt.plot(x, y, '.', marker = '^', alpha = 0.5)\n",
        "plt.plot(ex, b0 + b1*ex, color = 'green')\n",
        "plt.plot(ex, c0 + c1*ex + c2*ex**2, color = 'purple')\n",
        "plt.show()\n",
        "print(c2, c1, c0)\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "1.0012910147063707 -8.086824065070873 50.27052602037121\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "PufIjCGaXmAU"
      },
      "source": [
        "## **Projeto: simulação de um álbum de figurinhas**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iTybxsEjYEko",
        "colab_type": "text"
      },
      "source": [
        "### EXEMPLO: **Álbum Premier League 2019-2020**\n",
        "1. Total de cromos: **636**\n",
        "2. Preço do livro ilustrado capa brochura: **R\\$ 8,90**\n",
        "3. Envelope com 5 cromos: **R\\$ 2,50**\n",
        "\n",
        "### SUPOSIÇÕES\n",
        "1. Todas as figurinhas tem igual probabilidade de serem sorteradas\n",
        "2. Um pacotinho é comprado por vez  \n",
        "\n",
        "### ALGORITMO\n",
        "1. Comprar um pacotinho de figurinhas (5 figurinhas cada, que podem ser repetidas);\n",
        "2. Colar no álbum e verificar se o álbum está completo;\n",
        "3. Caso esteja incompleto, comprar mais um pacotinho, caso contrário, terminar.\n",
        "\n",
        "### PERGUNTAS\n",
        "1. Qual o valor médio investido para completar o álbum nessas condições?\n",
        "2. Quantos pacotes são necessários comprar, em média, para completar o álbum?\n",
        "3. Qual é a distribuição empírica do valor investido para completar o álbum?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "h2l9BcKaV_eX",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "n_album = 636\n",
        "preco_pacote = 2.50\n",
        "preco_album = 8.90\n",
        "simulacoes = 1000"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xB0munEeV_n_",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "\n",
        "# representação do álbum\n",
        "album = np.zeros(n_album) \n",
        "\n",
        "# representação do pacote de figurinhas\n",
        "pacotinho = np.random.choice(range(n_album), 5)\n",
        "pacotinho\n",
        "\n",
        "# 'colando' as figurinhas obtidas no álbum\n",
        "for i in pacotinho:\n",
        "    album[i] += 1"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "saOzUxjyoB6z",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "print(album)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Jvyn7lBTYEtO",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 36
        },
        "outputId": "5e2c5878-fda0-4437-dd7d-c05db7762be6"
      },
      "source": [
        "# comprando figurinhas até completar o álbum\n",
        "def SimulaAlbum():\n",
        "    album = np.zeros(n_album) \n",
        "    pacotes = 0\n",
        "    while not np.all(album > 0):\n",
        "        pacotinho = np.random.choice(range(n_album), 5)\n",
        "        pacotes += 1\n",
        "\n",
        "        for i in pacotinho:\n",
        "            album[i] += 1\n",
        " \n",
        "\n",
        "    valor_gasto = preco_album + preco_pacote * pacotes \n",
        "\n",
        "    return valor_gasto, pacotes\n",
        "\n",
        "SimulaAlbum()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(2178.9, 868)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 177
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "q1khZHjQoJhg",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 387
        },
        "outputId": "68d2b0ae-e1a9-4a4f-f067-11e20aecd599"
      },
      "source": [
        "valores = []\n",
        "for i in range(simulacoes):\n",
        "    valores.append(SimulaAlbum()[0])\n",
        "    if (i+1) % 50 == 0:\n",
        "        print('Simulação: ', i+1, '/', simulacoes)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Simulação:  50 / 1000\n",
            "Simulação:  100 / 1000\n",
            "Simulação:  150 / 1000\n",
            "Simulação:  200 / 1000\n",
            "Simulação:  250 / 1000\n",
            "Simulação:  300 / 1000\n",
            "Simulação:  350 / 1000\n",
            "Simulação:  400 / 1000\n",
            "Simulação:  450 / 1000\n",
            "Simulação:  500 / 1000\n",
            "Simulação:  550 / 1000\n",
            "Simulação:  600 / 1000\n",
            "Simulação:  650 / 1000\n",
            "Simulação:  700 / 1000\n",
            "Simulação:  750 / 1000\n",
            "Simulação:  800 / 1000\n",
            "Simulação:  850 / 1000\n",
            "Simulação:  900 / 1000\n",
            "Simulação:  950 / 1000\n",
            "Simulação:  1000 / 1000\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PM_3RPS5q_Z9",
        "colab_type": "text"
      },
      "source": [
        "As respostas das perguntas 1 e 2, respectivamente, são:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aWgOBRkHqoKk",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        },
        "outputId": "5c29a34c-6b92-41af-c5bd-30b88f7bee5e"
      },
      "source": [
        "print('O valor médio gasto foi:', round(np.mean(valores), 2))\n",
        "print('O numero de pacotes médio foi:', round((np.mean(valores) - preco_album)/preco_pacote, 2))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "O valor médio gasto foi: 2261.45\n",
            "O numero de pacotes médio foi: 901.02\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eFFhtwKkrF__",
        "colab_type": "text"
      },
      "source": [
        "Podemos visualizar a distribuição empírica do valor gasto através do **histograma** dos valores simulados"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-jMyRhC-rNim",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "outputId": "968df6f3-40fd-4da3-9e01-a7fdcb668c1d"
      },
      "source": [
        "plt.hist(valores, bins = 20, density = True, edgecolor = 'black')\n",
        "plt.title('Distribuição Empírica do Valor Gasto para Completar o Álbum')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "gOyFuZBwXmP9"
      },
      "source": [
        "## **Exercício 4**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "T1_xolefYFtX",
        "colab_type": "text"
      },
      "source": [
        "### Faça as modificações e implementações necessárias para responder as seguintes perguntas adicionais:\n",
        "\n",
        "4. Quantas vezes saiu a figurinha mais repetida, em média?\n",
        "5. Em média, quantas figurinhas não se repetem ao completar o álbum?\n",
        "6. Qual a probabilidade de se gastar mais que R\\$3000,00 para completar o álbum?\n",
        "7. Qual a probabilidade de se gastar menos que R\\$1500,00 para completar o álbum?\n",
        "8. Qual a probabilidade de se gastar mais do que a média para completar o álbum?\n",
        "9. Qual é o intervalo de confiança de 95% para o gasto ao se completar o álbum?\n",
        "10. Qual o valor médio gasto caso se esteja completando o álbum com mais um amigo?\n",
        "11. Quanto se economiza ao utilizar o cenário da questão 10?\n",
        "12. \n",
        "Qual o valor médio gasto caso se esteja completando o álbum com mais dois amigos?\n",
        "\n",
        "13. Quanto se economiza ao utilizar o cenário da questão 12?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1doFeZFoSCSM",
        "colab_type": "text"
      },
      "source": [
        "## **Exercício 5**\n",
        "\n",
        "Até hoje, na história da mega-sena, houve 2272 jogos. Faça um programa que simule o resultado de 2272 jogos da mega-sena. Se você tivesse feito um jogo simples em todos, qual o retorno esperado? Faça as suposições necessárias. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4KLNLxzOy5kq",
        "colab_type": "text"
      },
      "source": [
        "## **Links Úteis**\n",
        "- [Documentação do numpy](https://numpy.org/) "
      ]
    }
  ]
}