{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/financieras/pyCourse/blob/main/jupyter/calisto1/0590_matrices.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pyZjL_rfVuyX"
      },
      "source": [
        "# Matrices"
      ],
      "id": "pyZjL_rfVuyX"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jf51XtZRVuyc"
      },
      "source": [
        "Una matriz 4×5.  \n",
        "Cuatro filas, cinco columnas.  \n",
        "$$A_{(4×5)} =\n",
        "\\begin{pmatrix}\n",
        "a_{11} & a_{12} & a_{13} & a_{14} & a_{15} \\\\\n",
        "a_{21} & a_{22} & a_{23} & a_{24} & a_{25} \\\\\n",
        "a_{31} & a_{32} & a_{33} & a_{34} & a_{35} \\\\\n",
        "a_{41} & a_{42} & a_{43} & a_{44} & a_{45} \\\\\n",
        "\\end{pmatrix}\n",
        "$$"
      ],
      "id": "jf51XtZRVuyc"
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "KKV1-1faVuyh",
        "outputId": "3a24e667-183d-4df1-a334-990ff3f9a553",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1 3 4 \n",
            "4 5 6 \n",
            "7 8 9 \n"
          ]
        }
      ],
      "source": [
        "def imprimir(matriz):\n",
        "    for f in range(len(matriz)):\n",
        "        linea = \"\"\n",
        "        for c in range(len(matriz[f])):\n",
        "            linea += str(matriz[f][c]) + \" \"\n",
        "        print(linea)\n",
        "\n",
        "if __name__ == \"__main__\":\n",
        "    matriz = [\n",
        "        [1,3,4],\n",
        "        [4,5,6],\n",
        "        [7,8,9]\n",
        "    ]\n",
        "    imprimir(matriz)"
      ],
      "id": "KKV1-1faVuyh"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "D8uQgs_QVuyl"
      },
      "source": [
        "**Ejercicio**  \n",
        "En álgebra la [traza](https://es.wikipedia.org/wiki/Traza_(%C3%A1lgebra_lineal)) es la suma de la diagonal principal de una matriz.  \n",
        "Generar una matriz de números aleatorios y calcular su traza."
      ],
      "id": "D8uQgs_QVuyl"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FIcc9m-WVuyo"
      },
      "source": [
        "## Transponer una matriz"
      ],
      "id": "FIcc9m-WVuyo"
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Usando `zip`"
      ],
      "metadata": {
        "id": "K40IzJqm_5fx"
      },
      "id": "K40IzJqm_5fx"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "T3xKAXIXVuyp"
      },
      "source": [
        "Consideremos la siguiente matriz 3×4.  \n",
        "$$A_{(3×4)} =\n",
        "\\begin{pmatrix}\n",
        "a_{11} & a_{12} & a_{13} & a_{14} \\\\\n",
        "a_{21} & a_{22} & a_{23} & a_{24} \\\\\n",
        "a_{31} & a_{32} & a_{33} & a_{34}\n",
        "\\end{pmatrix} =\n",
        "\\begin{pmatrix}\n",
        "1 & 2 & 3 & 4 \\\\\n",
        "5 & 6 & 7 & 8 \\\\\n",
        "9 & 10 & 11 & 12\n",
        "\\end{pmatrix}\n",
        "$$"
      ],
      "id": "T3xKAXIXVuyp"
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "G_EWYNc3Vuyr",
        "outputId": "259d829f-8359-4a5f-a5a1-d7808472bb7d",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[(1, 5, 9), (2, 6, 10), (3, 7, 11), (4, 8, 12)]\n",
            "\n",
            "1 5 9\n",
            "2 6 10\n",
            "3 7 11\n",
            "4 8 12\n"
          ]
        }
      ],
      "source": [
        "matrix = [[1, 2, 3, 4],\n",
        "          [5, 6, 7, 8],\n",
        "          [9, 10, 11, 12]]\n",
        "\n",
        "m = list(zip(*matrix))\n",
        "\n",
        "print(m)   # m es una lista de tuplas\n",
        "print()\n",
        "\n",
        "for i in range(len(m)):\n",
        "    print(*m[i])"
      ],
      "id": "G_EWYNc3Vuyr"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IW6UqHOmVuyt"
      },
      "source": [
        "Su transpuesta es $A^{t}$ de dimensión 4×3.  \n",
        "$$A^{t} =\n",
        "\\begin{pmatrix}\n",
        "1 & 5 & 9 \\\\\n",
        "2 & 6 & 10 \\\\\n",
        "3 & 7 & 11 \\\\\n",
        "4 & 8 & 12\n",
        "\\end{pmatrix}  \n",
        "$$"
      ],
      "id": "IW6UqHOmVuyt"
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Transposición de una matriz permutando filas y columnas\n",
        "* Generamos la matriz m de números aleatorios, de dimensión 4x5\n",
        "* Son 4 filas y 5 columnas\n",
        "* Imprimimos m\n",
        "* Inicializamos la matriz transpuesta t de dimensión 5x4\n",
        "* Para crear t Invertimos las filas y columnas de m\n",
        "* Imprimimos la matriz transpuesta t"
      ],
      "metadata": {
        "id": "dPYDEuNRCEku"
      },
      "id": "dPYDEuNRCEku"
    },
    {
      "cell_type": "code",
      "source": [
        "# Transponer matrices\n",
        "from random import seed, randint\n",
        "seed()\n",
        "\n",
        "# inicializamos la matriz m de dimensines 4x5\n",
        "m = [[None]*5 for _ in range(4)]\n",
        "\n",
        "# generamos aleatoriamente la matriz m\n",
        "for i in range(4):\n",
        "    for j in range(5):\n",
        "        m[i][j] = randint(1,9)\n",
        "\n",
        "# imprimimos la matriz m\n",
        "for i in range(4):\n",
        "    for j in range(5):\n",
        "        print(m[i][j],end=\" \")\n",
        "    print()\n",
        "\n",
        "# inicializamos la matriz transpuesta t\n",
        "t = [[None]*len(m) for _ in range(len(m[0]))]\n",
        "\n",
        "for i in range(5):\n",
        "    for j in range(4):\n",
        "        t[i][j] = m[j][i]\n",
        "\n",
        "print()\n",
        "\n",
        "for i in range(5):   # esta forma de imprimir una matriz\n",
        "    print(*t[i])     # es más sencilla que la anterior"
      ],
      "metadata": {
        "id": "C-nqGaSqELJe",
        "outputId": "cb7b0107-3212-4daf-8026-3cb7a52f88fd",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "id": "C-nqGaSqELJe",
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "6 9 2 9 2 \n",
            "6 8 9 4 1 \n",
            "9 1 4 9 9 \n",
            "3 1 8 7 4 \n",
            "\n",
            "6 6 9 3\n",
            "9 8 1 1\n",
            "2 9 4 8\n",
            "9 4 9 7\n",
            "2 1 9 4\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Copia de matriz 2D\n",
        "Podemos copiar una matriz de dos dimensiones sin necesidad de llamar a la librería copy para usar la función deepcopy."
      ],
      "metadata": {
        "id": "P-yqNyEtGkEA"
      },
      "id": "P-yqNyEtGkEA"
    },
    {
      "cell_type": "code",
      "source": [
        "from random import seed, randint\n",
        "seed()\n",
        "\n",
        "# inicializamos la matriz m de dimensines 4x4\n",
        "m = [[None]*4 for _ in range(4)]\n",
        "\n",
        "# generamos aleatoriamente la matriz m\n",
        "for i in range(4):\n",
        "    for j in range(4):\n",
        "        m[i][j] = randint(1,9)\n",
        "\n",
        "# imprimimos la matriz m\n",
        "print(\"Matriz m\")\n",
        "for i in range(4):\n",
        "    for j in range(4):\n",
        "        print(m[i][j],end=\" \")\n",
        "    print()\n",
        "print()\n",
        "\n",
        "# creamos la matriz cm que es una copia de m\n",
        "cm = [row[:] for row in m]\n",
        "\n",
        "# alteramos el primer valor de m\n",
        "m[0][0] = 0\n",
        "\n",
        "# imprimimos m con su alteración\n",
        "print(\"Matriz m con el primer valor alterado\")\n",
        "for i in range(4): # este sistema es mejor\n",
        "    print(*m[i])   # para imprimir una matriz sin comas ni corchetes\n",
        "print()\n",
        "\n",
        "# imprimimos la copia y vemos que no se ha alterado\n",
        "print(\"La matriz copia de m es independiente, no tiene el valor alterado\")\n",
        "for i in range(4):\n",
        "    print(*cm[i])"
      ],
      "metadata": {
        "id": "PGYM9Lk_GlUI",
        "outputId": "d0dfef90-d7b2-49cd-c74f-11f51cf3a7cc",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "id": "PGYM9Lk_GlUI",
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Matriz m\n",
            "7 8 3 5 \n",
            "2 7 5 3 \n",
            "6 8 5 9 \n",
            "3 8 2 8 \n",
            "\n",
            "Matriz m con el primer valor alterado\n",
            "0 8 3 5\n",
            "2 7 5 3\n",
            "6 8 5 9\n",
            "3 8 2 8\n",
            "\n",
            "La matriz copia de m es independiente, no tiene el valor alterado\n",
            "7 8 3 5\n",
            "2 7 5 3\n",
            "6 8 5 9\n",
            "3 8 2 8\n"
          ]
        }
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
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    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.8.5"
    },
    "colab": {
      "name": "0590_matrices.ipynb",
      "provenance": [],
      "include_colab_link": true
    }
  },
  "nbformat": 4,
  "nbformat_minor": 5
}