02_numpy_annotations.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/OmarFloresPTY/my-google-colabs/blob/master/02_numpy_annotations.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "db32f457",
      "metadata": {
        "id": "db32f457"
      },
      "source": [
        "# Operaciones básicas de matriz con Numpy🧮\n",
        "Esta sección cubre sumas, restas, multiplicaciones, divisiones y más."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "596dc5ec",
      "metadata": {
        "id": "596dc5ec"
      },
      "outputs": [],
      "source": [
        "import numpy as np"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "cc1f62c0",
      "metadata": {
        "id": "cc1f62c0"
      },
      "source": [
        "<img src=\"https://numpy.org/doc/stable/_images/np_matrix_broadcasting.png\">"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "5a04260c",
      "metadata": {
        "id": "5a04260c",
        "outputId": "d22a2a98-7b8b-4057-cd98-271af4b9a5cb"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[ 1,  2,  3,  4],\n",
              "       [20, 21, 22, 23]])"
            ]
          },
          "execution_count": 9,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a = np.array([np.arange(1,5),np.arange(20,24)])\n",
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "87380e9a",
      "metadata": {
        "id": "87380e9a",
        "outputId": "7ebe5dde-620a-4e89-b41c-36c3cc33d485"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[1, 1, 1, 1],\n",
              "       [1, 1, 1, 1]])"
            ]
          },
          "execution_count": 10,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "b = np.ones((2,4),dtype=\"int32\")\n",
        "b"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "f16b730f",
      "metadata": {
        "id": "f16b730f",
        "outputId": "66004356-4b7a-4659-f327-bdfbafa2435e"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[ 2,  3,  4,  5],\n",
              "       [21, 22, 23, 24]])"
            ]
          },
          "execution_count": 16,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a + b #Suma de matrices"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "dbb45885",
      "metadata": {
        "id": "dbb45885",
        "outputId": "2d6f4a80-542a-4e32-c3c7-f7ab615ca2a7"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[ 0,  1,  2,  3],\n",
              "       [19, 20, 21, 22]])"
            ]
          },
          "execution_count": 17,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a - b #Resta de matrices"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "e7feffc4",
      "metadata": {
        "id": "e7feffc4",
        "outputId": "ebf34592-b8a7-4301-8480-7bc1efac918e"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[ 1,  2,  3,  4],\n",
              "       [20, 21, 22, 23]])"
            ]
          },
          "execution_count": 18,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a * b #Multiplicación de matrices"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "e6a74781",
      "metadata": {
        "scrolled": true,
        "id": "e6a74781",
        "outputId": "0b3188a7-e3e8-4616-e66a-4d9739a8d908"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[ 1.,  2.,  3.,  4.],\n",
              "       [20., 21., 22., 23.]])"
            ]
          },
          "execution_count": 19,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a / b #División de matrices"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "8fa19ade",
      "metadata": {
        "id": "8fa19ade"
      },
      "source": [
        "## Sumatoria de elementos"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "6f825e11",
      "metadata": {
        "scrolled": true,
        "id": "6f825e11",
        "outputId": "1a0e1ed1-8a26-476e-8132-35837866d0ac"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "96"
            ]
          },
          "execution_count": 23,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a.sum() #Default, suma todos los elementos de la matrices."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "aaf254cf",
      "metadata": {
        "id": "aaf254cf",
        "outputId": "0ea7e536-da69-45e4-d7fb-f08d308777f8"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([21, 23, 25, 27])"
            ]
          },
          "execution_count": 24,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a.sum(axis=0) #Suma solo las columnas"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "e69d238a",
      "metadata": {
        "id": "e69d238a",
        "outputId": "b06e8ff7-5d61-40bf-f80f-a70aff0d5dfc"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([10, 86])"
            ]
          },
          "execution_count": 25,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a.sum(axis=1) #Suma solo las filas"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "73cccdbc",
      "metadata": {
        "id": "73cccdbc"
      },
      "source": [
        "## Producto Escalar"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "73da3024",
      "metadata": {
        "id": "73da3024",
        "outputId": "65a4074d-2eed-4077-c007-5dad16a60a05"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[ 1,  2,  3,  4],\n",
              "       [20, 21, 22, 23]])"
            ]
          },
          "execution_count": 26,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "63a37b77",
      "metadata": {
        "id": "63a37b77",
        "outputId": "54e5a70e-c6ce-45ac-d1a0-89043fb4482f"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[ 2,  4,  6,  8],\n",
              "       [40, 42, 44, 46]])"
            ]
          },
          "execution_count": 27,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a * 2"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "13064a36",
      "metadata": {
        "id": "13064a36"
      },
      "source": [
        "# Operaciones de matriz más útiles 🧑‍🔬🧠\n",
        "Esta sección cubre máximo, mínimo, suma, media, producto, desviación estándar y más"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "2f097c57",
      "metadata": {
        "id": "2f097c57"
      },
      "source": [
        "<img src=\"https://numpy.org/doc/stable/_images/np_matrix_aggregation.png\">"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "ab9ec8d2",
      "metadata": {
        "id": "ab9ec8d2"
      },
      "source": [
        "<img src=\"https://numpy.org/doc/stable/_images/np_matrix_aggregation_row.png\">"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "bc2456ed",
      "metadata": {
        "id": "bc2456ed"
      },
      "outputs": [],
      "source": [
        "a = np.array([[0.45053314, 0.17296777, 0.34376245, 0.5510652],\n",
        "              [0.54627315, 0.05093587, 0.40067661, 0.55645993],\n",
        "              [0.12697628, 0.82485143, 0.26590556, 0.56917101]])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "ad272f2a",
      "metadata": {
        "id": "ad272f2a",
        "outputId": "11cfdaed-ec07-4047-c082-d11a82dba8f2"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "4.8595784"
            ]
          },
          "execution_count": 41,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a.sum()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "f8246276",
      "metadata": {
        "id": "f8246276",
        "outputId": "5aca9d12-eb42-4374-ede6-54877280429f"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0.82485143"
            ]
          },
          "execution_count": 44,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a.max() #Trae el dato más grande de la matriz"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "6e6a3268",
      "metadata": {
        "id": "6e6a3268",
        "outputId": "9998a52b-1302-4513-c23a-03b763380edc"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([0.54627315, 0.82485143, 0.40067661, 0.56917101])"
            ]
          },
          "execution_count": 47,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a.max(axis=0) #Encuentra el mayor de cada columna"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "9137bf77",
      "metadata": {
        "id": "9137bf77",
        "outputId": "7a38e372-dab1-430b-d28c-c93d85648788"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([0.5510652 , 0.55645993, 0.82485143])"
            ]
          },
          "execution_count": 48,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a.max(axis=1) #Encuentra el mayor de cada fila"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "e1af304e",
      "metadata": {
        "scrolled": true,
        "id": "e1af304e",
        "outputId": "5256b8ca-2e3c-44f8-a07f-5db40827b31d"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0.05093587"
            ]
          },
          "execution_count": 45,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a.min() #Trae el dato más pequeño de la matriz, al igual que que max podemos encontrar el min por fila y columna."
      ]
    },
    {
      "cell_type": "markdown",
      "id": "9ed2c04b",
      "metadata": {
        "id": "9ed2c04b"
      },
      "source": [
        "## Generar números aleatorios"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "a99e461a",
      "metadata": {
        "id": "a99e461a"
      },
      "outputs": [],
      "source": [
        "a_rand = np.random.random((3,2,3)) #Los números están en el rango [0,1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "b3c09e41",
      "metadata": {
        "id": "b3c09e41",
        "outputId": "09a363f2-91bf-4bc8-bc23-00b08f17d528"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[[0.33831789, 0.50024697, 0.94628129],\n",
              "        [0.62803167, 0.7908523 , 0.07457066]],\n",
              "\n",
              "       [[0.60193675, 0.61083423, 0.32835821],\n",
              "        [0.99464995, 0.43230278, 0.24431742]],\n",
              "\n",
              "       [[0.83866818, 0.35581608, 0.81439501],\n",
              "        [0.44611245, 0.71511959, 0.50399673]]])"
            ]
          },
          "execution_count": 83,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a_rand"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "a2d22e9f",
      "metadata": {
        "id": "a2d22e9f",
        "outputId": "4959d616-ad7a-42d8-ed3d-18ccd70003d9"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0.2077438820341544"
            ]
          },
          "execution_count": 84,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "random_rand = np.random.rand() #Genera solo un número aleatorio en el rango [0,1)\n",
        "random_rand"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "ca57ecaf",
      "metadata": {
        "scrolled": true,
        "id": "ca57ecaf",
        "outputId": "6b142f74-fbd5-42bf-be96-d70ff9e5d706"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[0, 5, 6, 5],\n",
              "       [5, 9, 6, 1],\n",
              "       [4, 9, 8, 6],\n",
              "       [3, 6, 6, 3]])"
            ]
          },
          "execution_count": 85,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "random03 = np.random.randint(0,10,size=(4,4))\n",
        "random03"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "082df40b",
      "metadata": {
        "id": "082df40b"
      },
      "source": [
        "## Cómo obtener artículos únicos y recuentos\n",
        "Esta sección cubre np.unique(), funciona para vectores y matrices"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "2572dddc",
      "metadata": {
        "id": "2572dddc"
      },
      "outputs": [],
      "source": [
        "a = np.array([11, 11, 12, 13, 14, 15, 16, 17, 12, 13, 11, 14, 18, 19, 20])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "53e8a207",
      "metadata": {
        "id": "53e8a207",
        "outputId": "0b012a35-3232-406e-b1b5-0fc071ab0222"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([11, 12, 13, 14, 15, 16, 17, 18, 19, 20])"
            ]
          },
          "execution_count": 94,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "val_unicos, conteo_repetidos = np.unique(a, return_counts = True) #Si solo queremos los valores únicos, quitamos el segundo parámetro\n",
        "val_unicos"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "c6a57016",
      "metadata": {
        "id": "c6a57016",
        "outputId": "4f174d6c-c3f8-4a32-b8f4-8fe7df1a965a"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([3, 2, 2, 2, 1, 1, 1, 1, 1, 1], dtype=int64)"
            ]
          },
          "execution_count": 95,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "conteo_repetidos"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "1010176f",
      "metadata": {
        "scrolled": true,
        "id": "1010176f",
        "outputId": "d110baae-780a-4e32-dc6b-7417c9d9e2dd"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[(11, 3),\n",
              " (12, 2),\n",
              " (13, 2),\n",
              " (14, 2),\n",
              " (15, 1),\n",
              " (16, 1),\n",
              " (17, 1),\n",
              " (18, 1),\n",
              " (19, 1),\n",
              " (20, 1)]"
            ]
          },
          "execution_count": 96,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "list(zip(val_unicos,conteo_repetidos))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "9c74afd0",
      "metadata": {
        "id": "9c74afd0",
        "outputId": "c33a7548-4c94-4c84-fb97-a3c403057e9f"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[ 1,  2,  3,  4],\n",
              "       [ 5,  6,  7,  8],\n",
              "       [ 9, 10, 11, 12],\n",
              "       [ 1,  2,  3,  4]])"
            ]
          },
          "execution_count": 114,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a_2d = np.array([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [1, 2, 3, 4]])\n",
        "a_2d"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "152753ab",
      "metadata": {
        "id": "152753ab",
        "outputId": "5904b02e-d9b3-496f-c584-6ae370993530"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[ 1  2  3  4  5  6  7  8  9 10 11 12]\n",
            "(12,)\n"
          ]
        }
      ],
      "source": [
        "a_2d_unicos = np.unique(a_2d)\n",
        "print(a_2d_unicos)\n",
        "print(a_2d_unicos.shape) #IMPORTANTE! Al sacar los repetidos, se convierte en un array"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "5f03ba24",
      "metadata": {
        "scrolled": false,
        "id": "5f03ba24",
        "outputId": "3c047f01-96ba-4745-93d2-7ecdcb94f1c3"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[ 1,  2,  3,  4],\n",
              "       [ 5,  6,  7,  8],\n",
              "       [ 9, 10, 11, 12]])"
            ]
          },
          "execution_count": 116,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a_2d_unicos_columns = np.unique(a_2d,axis=0) #Se especifica que se encuentre los valores únicos por columna\n",
        "a_2d_unicos_columns"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "0a025938",
      "metadata": {
        "id": "0a025938",
        "outputId": "0f1255ba-47be-46cc-80fa-8397c0ac7ce1"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[ 1,  2,  4,  4],\n",
              "       [ 5,  6,  8,  8],\n",
              "       [ 9, 10, 12, 12],\n",
              "       [ 1,  2,  4,  4]])"
            ]
          },
          "execution_count": 117,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a_2d = np.array([[1, 2, 4, 4], [5, 6, 8, 8], [9, 10, 12, 12], [1, 2, 4, 4]])\n",
        "a_2d"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "5da47a96",
      "metadata": {
        "id": "5da47a96",
        "outputId": "6002c8d0-dd51-4dd1-9ac4-8d7dc986e4a8"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[ 1,  2,  4],\n",
              "       [ 5,  6,  8],\n",
              "       [ 9, 10, 12],\n",
              "       [ 1,  2,  4]])"
            ]
          },
          "execution_count": 122,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a_2d_unicos_rows = np.unique(a_2d,axis=1) #Se especifica que se encuentre los valores únicos por columna\n",
        "a_2d_unicos_rows"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "8d64a42b",
      "metadata": {
        "id": "8d64a42b"
      },
      "source": [
        "## Transponer y remodelar una matriz\n",
        "<img src=\"https://numpy.org/doc/stable/_images/np_transposing_reshaping.png\">"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "1954ca44",
      "metadata": {
        "id": "1954ca44",
        "outputId": "71752105-a807-4183-bec7-650bc209dc0b"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([1, 2, 3, 4, 5, 6])"
            ]
          },
          "execution_count": 125,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "data = np.arange(1,7)\n",
        "data"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "011b5d02",
      "metadata": {
        "id": "011b5d02",
        "outputId": "4f6fd9ff-155f-4bb5-dc64-b25e38e56036"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(6,)"
            ]
          },
          "execution_count": 127,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "data.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "5df30f54",
      "metadata": {
        "id": "5df30f54",
        "outputId": "5155268c-73ea-41f4-ce35-67d6d26715c5"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[1, 2, 3],\n",
              "       [4, 5, 6]])"
            ]
          },
          "execution_count": 133,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "data.reshape(2,3)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "fb1c5ce7",
      "metadata": {
        "id": "fb1c5ce7",
        "outputId": "51620165-bd5e-4b4a-c323-7e698f00497f"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[1, 4],\n",
              "       [2, 5],\n",
              "       [3, 6]])"
            ]
          },
          "execution_count": 132,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "data.reshape(2,3).T"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "65d5acb3",
      "metadata": {
        "id": "65d5acb3"
      },
      "source": [
        "## Cómo invertir una matriz\n",
        "Esta sección cubre np.flip()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "c747bd29",
      "metadata": {
        "id": "c747bd29",
        "outputId": "effe9f2b-3882-4604-a8c2-1930fce71b29",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1, 2, 3, 4, 5, 6, 7, 8])"
            ]
          },
          "metadata": {},
          "execution_count": 2
        }
      ],
      "source": [
        "arr = np.array([1, 2, 3, 4, 5, 6, 7, 8])\n",
        "arr"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "arr_invertido = np.flip(arr)\n",
        "arr_invertido"
      ],
      "metadata": {
        "id": "oNMHL2zt4Kp8",
        "outputId": "15c6051d-1916-4176-bc24-d85c6bf2f878",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "id": "oNMHL2zt4Kp8",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([8, 7, 6, 5, 4, 3, 2, 1])"
            ]
          },
          "metadata": {},
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "arr_2d = np.array([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]])\n",
        "arr_2d"
      ],
      "metadata": {
        "id": "iG_wbo7d4bpk",
        "outputId": "d2fcbcd8-aa6d-4210-8f28-f60e5210d6d2",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "id": "iG_wbo7d4bpk",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 1,  2,  3,  4],\n",
              "       [ 5,  6,  7,  8],\n",
              "       [ 9, 10, 11, 12]])"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "arr_2d_invertido = np.flip(arr_2d)\n",
        "arr_2d_invertido #Invierto totalmente la matriz, tanto columnas como filas."
      ],
      "metadata": {
        "id": "PonwMkfb4fBn",
        "outputId": "8fc50ef8-01ab-45bc-a6b1-cf0cdaa4287d",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "id": "PonwMkfb4fBn",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[12, 11, 10,  9],\n",
              "       [ 8,  7,  6,  5],\n",
              "       [ 4,  3,  2,  1]])"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "arr_2d_invertido = np.flip(arr_2d,axis=0) #Solo se invierten las columnas\n",
        "arr_2d_invertido"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MUgMBV0Y7z6i",
        "outputId": "ee67bb82-acf0-4be4-98f3-d116dabacd2d"
      },
      "id": "MUgMBV0Y7z6i",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 9, 10, 11, 12],\n",
              "       [ 5,  6,  7,  8],\n",
              "       [ 1,  2,  3,  4]])"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "arr_2d_invertido = np.flip(arr_2d,axis=1) #Solo se invierten las filas\n",
        "arr_2d_invertido"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "CcNiAjpd8M4y",
        "outputId": "8bb4a95d-ad80-4fe3-e08d-b72a95a0fcf5"
      },
      "id": "CcNiAjpd8M4y",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 4,  3,  2,  1],\n",
              "       [ 8,  7,  6,  5],\n",
              "       [12, 11, 10,  9]])"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "arr_2d[1] = np.flip(arr_2d[1]) #Invertir solo una fila\n",
        "arr_2d"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zSDvz_uP9P0P",
        "outputId": "0ec1fbe3-7433-4af6-cfac-eaa81b188515"
      },
      "id": "zSDvz_uP9P0P",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 1,  2,  3,  4],\n",
              "       [ 8,  7,  6,  5],\n",
              "       [ 9, 10, 11, 12]])"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "arr_2d[:,1] = np.flip(arr_2d[:,1]) #Invertir solo una columna\n",
        "arr_2d"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Re9P8ALO9kd1",
        "outputId": "163f1ba4-ee08-4155-eef0-53567f5636f5"
      },
      "id": "Re9P8ALO9kd1",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 1, 10,  3,  4],\n",
              "       [ 8,  7,  6,  5],\n",
              "       [ 9,  2, 11, 12]])"
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Reformar y aplanar matrices multimensionales.\n",
        "Uso de flateen() y ravel(). La diferencia entre ambos es que ravel() los cambios afectarán a la matriz principal."
      ],
      "metadata": {
        "id": "mw8GJc2VC1Hp"
      },
      "id": "mw8GJc2VC1Hp"
    },
    {
      "cell_type": "code",
      "source": [
        "x = np.array([[1 , 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]])\n",
        "x"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Crk2CG_jC6Dc",
        "outputId": "25847bbb-d580-48c1-8df8-d4a2255c0f58"
      },
      "id": "Crk2CG_jC6Dc",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 1,  2,  3,  4],\n",
              "       [ 5,  6,  7,  8],\n",
              "       [ 9, 10, 11, 12]])"
            ]
          },
          "metadata": {},
          "execution_count": 21
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x.size"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gWLML8ZMC87R",
        "outputId": "2e114b5c-9160-4d91-88d1-7c3e8a26be30"
      },
      "id": "gWLML8ZMC87R",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "12"
            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x.flatten() #Aplana una matriz"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-GEQCzLFDFOu",
        "outputId": "25ea1582-b512-4f80-9a4e-31a472e95eed"
      },
      "id": "-GEQCzLFDFOu",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12])"
            ]
          },
          "metadata": {},
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x.ravel() #Aplana una matriz"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "NquhaIe1DmuT",
        "outputId": "8f572fc6-f874-4ef1-a90a-a574f9fa4f49"
      },
      "id": "NquhaIe1DmuT",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12])"
            ]
          },
          "metadata": {},
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x_ref = x.flatten()\n",
        "x_ref[0] = 10000 #Referencia\n",
        "x_ref,x #No afectada la matriz principal"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "OmY5OI25Du98",
        "outputId": "ee1585fe-3880-4aaa-f05a-466fe817d017"
      },
      "id": "OmY5OI25Du98",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([10000,     2,     3,     4,     5,     6,     7,     8,     9,\n",
              "           10,    11,    12]),\n",
              " array([[10000,     2,     3,     4],\n",
              "        [    5,     6,     7,     8],\n",
              "        [    9,    10,    11,    12]]))"
            ]
          },
          "metadata": {},
          "execution_count": 30
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x_ref = x.ravel()\n",
        "x_ref[0] = 10000 #Referencia\n",
        "x_ref,x #Afectada la matriz principal"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vrlj560pD1Kq",
        "outputId": "d7ca8a6d-5fca-42cb-9b05-ccf7b6c84e8e"
      },
      "id": "vrlj560pD1Kq",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([10000,     2,     3,     4,     5,     6,     7,     8,     9,\n",
              "           10,    11,    12]),\n",
              " array([[10000,     2,     3,     4],\n",
              "        [    5,     6,     7,     8],\n",
              "        [    9,    10,    11,    12]]))"
            ]
          },
          "metadata": {},
          "execution_count": 31
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Acceder a la documentación para más información. 📖"
      ],
      "metadata": {
        "id": "m1G1S2CHGMiL"
      },
      "id": "m1G1S2CHGMiL"
    },
    {
      "cell_type": "code",
      "source": [
        "help(max)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "HrGNkAkRGXXr",
        "outputId": "ea59c14a-df43-4c77-ea8a-feee7aee0127"
      },
      "id": "HrGNkAkRGXXr",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Help on built-in function max in module builtins:\n",
            "\n",
            "max(...)\n",
            "    max(iterable, *[, default=obj, key=func]) -> value\n",
            "    max(arg1, arg2, *args, *[, key=func]) -> value\n",
            "    \n",
            "    With a single iterable argument, return its biggest item. The\n",
            "    default keyword-only argument specifies an object to return if\n",
            "    the provided iterable is empty.\n",
            "    With two or more arguments, return the largest argument.\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "help(np.random.randint)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "p30khKG5Gprd",
        "outputId": "df7a755e-4e54-461b-cde2-ab67d2bd429d"
      },
      "id": "p30khKG5Gprd",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Help on built-in function randint:\n",
            "\n",
            "randint(...) method of numpy.random.mtrand.RandomState instance\n",
            "    randint(low, high=None, size=None, dtype=int)\n",
            "    \n",
            "    Return random integers from `low` (inclusive) to `high` (exclusive).\n",
            "    \n",
            "    Return random integers from the \"discrete uniform\" distribution of\n",
            "    the specified dtype in the \"half-open\" interval [`low`, `high`). If\n",
            "    `high` is None (the default), then results are from [0, `low`).\n",
            "    \n",
            "    .. note::\n",
            "        New code should use the ``integers`` method of a ``default_rng()``\n",
            "        instance instead; please see the :ref:`random-quick-start`.\n",
            "    \n",
            "    Parameters\n",
            "    ----------\n",
            "    low : int or array-like of ints\n",
            "        Lowest (signed) integers to be drawn from the distribution (unless\n",
            "        ``high=None``, in which case this parameter is one above the\n",
            "        *highest* such integer).\n",
            "    high : int or array-like of ints, optional\n",
            "        If provided, one above the largest (signed) integer to be drawn\n",
            "        from the distribution (see above for behavior if ``high=None``).\n",
            "        If array-like, must contain integer values\n",
            "    size : int or tuple of ints, optional\n",
            "        Output shape.  If the given shape is, e.g., ``(m, n, k)``, then\n",
            "        ``m * n * k`` samples are drawn.  Default is None, in which case a\n",
            "        single value is returned.\n",
            "    dtype : dtype, optional\n",
            "        Desired dtype of the result. Byteorder must be native.\n",
            "        The default value is int.\n",
            "    \n",
            "        .. versionadded:: 1.11.0\n",
            "    \n",
            "    Returns\n",
            "    -------\n",
            "    out : int or ndarray of ints\n",
            "        `size`-shaped array of random integers from the appropriate\n",
            "        distribution, or a single such random int if `size` not provided.\n",
            "    \n",
            "    See Also\n",
            "    --------\n",
            "    random_integers : similar to `randint`, only for the closed\n",
            "        interval [`low`, `high`], and 1 is the lowest value if `high` is\n",
            "        omitted.\n",
            "    Generator.integers: which should be used for new code.\n",
            "    \n",
            "    Examples\n",
            "    --------\n",
            "    >>> np.random.randint(2, size=10)\n",
            "    array([1, 0, 0, 0, 1, 1, 0, 0, 1, 0]) # random\n",
            "    >>> np.random.randint(1, size=10)\n",
            "    array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])\n",
            "    \n",
            "    Generate a 2 x 4 array of ints between 0 and 4, inclusive:\n",
            "    \n",
            "    >>> np.random.randint(5, size=(2, 4))\n",
            "    array([[4, 0, 2, 1], # random\n",
            "           [3, 2, 2, 0]])\n",
            "    \n",
            "    Generate a 1 x 3 array with 3 different upper bounds\n",
            "    \n",
            "    >>> np.random.randint(1, [3, 5, 10])\n",
            "    array([2, 2, 9]) # random\n",
            "    \n",
            "    Generate a 1 by 3 array with 3 different lower bounds\n",
            "    \n",
            "    >>> np.random.randint([1, 5, 7], 10)\n",
            "    array([9, 8, 7]) # random\n",
            "    \n",
            "    Generate a 2 by 4 array using broadcasting with dtype of uint8\n",
            "    \n",
            "    >>> np.random.randint([1, 3, 5, 7], [[10], [20]], dtype=np.uint8)\n",
            "    array([[ 8,  6,  9,  7], # random\n",
            "           [ 1, 16,  9, 12]], dtype=uint8)\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Cómo guardar y cargar objetos NumPy💾\n",
        "np.save() para almacenar solo un objeto ndarray y np.savez() para almacenar más de un objeto ndarray en un mismo archivo."
      ],
      "metadata": {
        "id": "KdkisR2rHT8-"
      },
      "id": "KdkisR2rHT8-"
    },
    {
      "cell_type": "code",
      "source": [
        "a = np.array([1, 2, 3, 4, 5, 6])"
      ],
      "metadata": {
        "id": "yekoGhjVHXll"
      },
      "id": "yekoGhjVHXll",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "np.save('ejemplo01',a) #Guarda el archivo en formato .npy"
      ],
      "metadata": {
        "id": "rHsP9WzRu4hd"
      },
      "id": "rHsP9WzRu4hd",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "b = np.load('ejemplo01.npy')"
      ],
      "metadata": {
        "id": "mRSRhjGrvEMP"
      },
      "id": "mRSRhjGrvEMP",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "b"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ee0W7Cs3vSkp",
        "outputId": "68c7c038-dc73-4542-df49-9cf65862c064"
      },
      "id": "ee0W7Cs3vSkp",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1, 2, 3, 4, 5, 6])"
            ]
          },
          "metadata": {},
          "execution_count": 45
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "csv_arr = np.array([1, 2, 3, 4, 5, 6, 7, 8])"
      ],
      "metadata": {
        "id": "W1SNFeJFvajz"
      },
      "id": "W1SNFeJFvajz",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "np.savetxt('ejemplo02.csv',csv_arr) #Guardar matriz en un csv y txt"
      ],
      "metadata": {
        "id": "rs73fBvoveJ8"
      },
      "id": "rs73fBvoveJ8",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "np.loadtxt('ejemplo02.csv') #cargar matriz de un csv y txt"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "RuX24senvmEz",
        "outputId": "55f504f5-f5d1-4750-d1e7-b652bea773bd"
      },
      "id": "RuX24senvmEz",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1., 2., 3., 4., 5., 6., 7., 8.])"
            ]
          },
          "metadata": {},
          "execution_count": 48
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Importación y exportación de un CSV 📎"
      ],
      "metadata": {
        "id": "HehPo4Tbw4dr"
      },
      "id": "HehPo4Tbw4dr"
    },
    {
      "cell_type": "code",
      "source": [
        "import pandas as pd"
      ],
      "metadata": {
        "id": "bW7ihWhwz0Kh"
      },
      "id": "bW7ihWhwz0Kh",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "a = np.array([[-2.58289208,  0.43014843, -1.24082018, 1.59572603],\n",
        "              [ 0.99027828, 1.17150989,  0.94125714, -0.14692469],\n",
        "              [ 0.76989341,  0.81299683, -0.95068423, 0.11769564],\n",
        "              [ 0.20484034,  0.34784527,  1.96979195, 0.51992837]])\n",
        "a"
      ],
      "metadata": {
        "id": "RSoC6zcgw9Kw",
        "outputId": "069e0614-12e3-41e8-b3af-c4de47adf365",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "id": "RSoC6zcgw9Kw",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-2.58289208,  0.43014843, -1.24082018,  1.59572603],\n",
              "       [ 0.99027828,  1.17150989,  0.94125714, -0.14692469],\n",
              "       [ 0.76989341,  0.81299683, -0.95068423,  0.11769564],\n",
              "       [ 0.20484034,  0.34784527,  1.96979195,  0.51992837]])"
            ]
          },
          "metadata": {},
          "execution_count": 50
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "df = pd.DataFrame(a)\n",
        "df"
      ],
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        "outputId": "66f33a1e-9b9b-4ae1-c492-90c752f37296",
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          "height": 175
        }
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      "id": "QSjE6-SezyQB",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
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            "text/plain": [
              "          0         1         2         3\n",
              "0 -2.582892  0.430148 -1.240820  1.595726\n",
              "1  0.990278  1.171510  0.941257 -0.146925\n",
              "2  0.769893  0.812997 -0.950684  0.117696\n",
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              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
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              "\n",
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              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
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              "  "
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          "metadata": {},
          "execution_count": 53
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      ]
    },
    {
      "cell_type": "code",
      "source": [
        "df.to_csv('ejemplo03.csv') #Método Pandas para guardar la matriz"
      ],
      "metadata": {
        "id": "Sg4vWT0Dz-ZS"
      },
      "id": "Sg4vWT0Dz-ZS",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "data = pd.read_csv('ejemplo03.csv') #Método Panas para leer la matriz guardada.\n",
        "data"
      ],
      "metadata": {
        "id": "RZvBhYxd0C5X",
        "outputId": "30f750c3-ab58-4152-93f9-7aadac3dc084",
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          "base_uri": "https://localhost:8080/",
          "height": 175
        }
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      "id": "RZvBhYxd0C5X",
      "execution_count": null,
      "outputs": [
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          "data": {
            "text/plain": [
              "   Unnamed: 0         0         1         2         3\n",
              "0           0 -2.582892  0.430148 -1.240820  1.595726\n",
              "1           1  0.990278  1.171510  0.941257 -0.146925\n",
              "2           2  0.769893  0.812997 -0.950684  0.117696\n",
              "3           3  0.204840  0.347845  1.969792  0.519928"
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              "\n",
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              "\n",
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              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
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              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-50910d51-2090-412c-b1c2-b3c86b240f81 button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-50910d51-2090-412c-b1c2-b3c86b240f81');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
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              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
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              "  </div>\n",
              "  "
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          },
          "metadata": {},
          "execution_count": 62
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "np.savetxt('ejemplo04.csv',a,fmt='%.2f', delimiter=',',header='1, 2, 3, 4') #Método numpy para guardar la matriz"
      ],
      "metadata": {
        "id": "uupd5gps0Ub0"
      },
      "id": "uupd5gps0Ub0",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "b = pd.read_csv('ejemplo04.csv')\n",
        "b"
      ],
      "metadata": {
        "id": "GcYcm1v64SnK",
        "outputId": "323bf7d2-2eab-48a9-c961-236581e7ddbd",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 175
        }
      },
      "id": "GcYcm1v64SnK",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "    # 1     2     3     4\n",
              "0 -2.58  0.43 -1.24  1.60\n",
              "1  0.99  1.17  0.94 -0.15\n",
              "2  0.77  0.81 -0.95  0.12\n",
              "3  0.20  0.35  1.97  0.52"
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              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th># 1</th>\n",
              "      <th>2</th>\n",
              "      <th>3</th>\n",
              "      <th>4</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>-2.58</td>\n",
              "      <td>0.43</td>\n",
              "      <td>-1.24</td>\n",
              "      <td>1.60</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0.99</td>\n",
              "      <td>1.17</td>\n",
              "      <td>0.94</td>\n",
              "      <td>-0.15</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0.77</td>\n",
              "      <td>0.81</td>\n",
              "      <td>-0.95</td>\n",
              "      <td>0.12</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0.20</td>\n",
              "      <td>0.35</td>\n",
              "      <td>1.97</td>\n",
              "      <td>0.52</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-0c26e1db-2c0c-4d9b-9d68-57ae7fc44c5d')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-0c26e1db-2c0c-4d9b-9d68-57ae7fc44c5d button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-0c26e1db-2c0c-4d9b-9d68-57ae7fc44c5d');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 68
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Trazado de matrices con Matplotlib 📊📉"
      ],
      "metadata": {
        "id": "OrIng310448k"
      },
      "id": "OrIng310448k"
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt"
      ],
      "metadata": {
        "id": "FZtfaKKb50m7"
      },
      "id": "FZtfaKKb50m7",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "a = np.array([2, 1, 5, 7, 4, 6, 8, 14, 10, 9, 18, 20, 22])"
      ],
      "metadata": {
        "id": "yQXmLuBI49vg"
      },
      "id": "yQXmLuBI49vg",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(a)\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "Z-zrrLlZ5zSg",
        "outputId": "b1308a7f-8dbd-4f53-f2e9-1b75bddf0cb4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        }
      },
      "id": "Z-zrrLlZ5zSg",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x = np.linspace(0,5,20)\n",
        "y = np.linspace(0,10,20)"
      ],
      "metadata": {
        "id": "StsSYibW6NjX"
      },
      "id": "StsSYibW6NjX",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(x,y,'purple')\n",
        "plt.plot(x,y,'o')"
      ],
      "metadata": {
        "id": "EUH0g_Rs6VNt",
        "outputId": "3e0eded6-f11a-4ee6-d715-baed159fdad2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        }
      },
      "id": "EUH0g_Rs6VNt",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fa9893ee8c0>]"
            ]
          },
          "metadata": {},
          "execution_count": 73
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3 (ipykernel)",
      "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": "3.11.4"
    },
    "colab": {
      "provenance": [],
      "toc_visible": true,
      "include_colab_link": true
    }
  },
  "nbformat": 4,
  "nbformat_minor": 5
}