{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Y7JgKfzlPBrr"
   },
   "source": [
    "![taller_python](https://github.com/fifabsas/talleresfifabsas/blob/master/python/2_Numerico/fig/logo_fifa.png?raw=true)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "os_60KoG9612"
   },
   "source": [
    "# Taller de Python Capítulo 2:  Numérico y Laboratorio\n",
    "[Link al notebook en Google Colaboratory](https://drive.google.com/file/d/14aLUlUl4zZwm7eyVep_zQKFzBPx83lfz/view?usp=sharing)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "w5EORpIB961-"
   },
   "source": [
    "## Nuestra motivación para hoy\n",
    "De la última clase, tenemos herramientas básicas de Python que tienen muchisimas aplicaciones. Hoy vamos a ver como se puede usar Python para analizar datos de una caida libre. Digamos que en su laboratorio adquirieron los datos de la posición de una pelotita en distintos tiempos, luego de haberla soltado a una altura de 100 metros. Ahora, quieren cargar estos datos a un programa de Python, visualizarlos, y obtener el valor de la gravedad $g$.\n",
    "\n",
    "Vamos a ver algunas herramientas que nos permitirán llevar esto a cabo."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "jTt04ORN961_"
   },
   "source": [
    "---\n",
    "\n",
    "## Bibliotecas\n",
    "Ya hemos visto la vez anterior que Python tiene varias funciones que vienen \"de fábrica\" como `help()`, `print()` así también como operaciones básicas entre números como sumar, restar, etc; también vimos que nosotros podemos crear nustras propias funciones para que hagan lo que necesitemos usando la palabra clave `def nombre_funcion`. Si uno necesita siempre realizar las mismas operaciones, reutilizará la misma función en todos sus códigos.\n",
    "\n",
    "Por ejemplo: Supongamos que uno quiere calcular `cos(x)`. Python no viene por defecto con esa operación, uno debería crear un algoritmo (es decir, una serie de acciones) que calcule el valor del cos de x (cosa que puede ser no trivial), pero es _obvio_ que alguien ya lo hizo antes, alguien ya pensó el algoritmo, lo escribió, y lo utiliza diariamente, si esta persona subió su código a internet, todos podemos aprovechar y utilizarlo sin preocuparnos en cómo hizo esta persona!! Solamente hay que decirle a Python _donde_ es que está guardado esta función. **Esta posibilidad de usar algoritmos de otros es fundamental en la programación, porque es lo que permite que nuestro problema se limite solamente a entender cómo llamar a estos algoritmos ya pensados y no tener que pensarlos cada vez**.\n",
    "\n",
    "Vamos entonces a decirle a Python que, además de sus operaciones de fábrica, queremos ampliar nuestro abanico de operaciones matemáticas en todas las opciones que aparecen dentro de la biblioteca \"math\" (una biblioteca es, tal como sugiere el nombre, un archivo con un montón de funciones, objetos y demás).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "AJQnKcwW962B"
   },
   "outputs": [],
   "source": [
    "import math  # Importo a mi programa todo lo que este contenido dentro del archivo \"math\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "swNFXCSM962D"
   },
   "source": [
    "Con esta linea Python entiende que queremos que traiga todo lo que está dentro del archivo \"math\"\n",
    "\n",
    "###### <span style='color:red'>OJO:</span> No todas las bibliotecas vienen instaladas por defecto, si queremos usar una muy rara es probable que tengamos que instalarla nosotros. Las que vamos a utilizar en el curso ya vienen instaladas por Google en Colaboratory o fueron instaladas automaticamente por Anaconda en su computadora.\n",
    "\n",
    "Macanudo, ahora que Python trajo esa biblioteca, nosotros podemos acceder a su contenido usando la sintaxis ```math.lo_que_haya_dentro_de_math``` por ejemplo, ```math.cos()```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "id": "iGzP4335962E"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.cos(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Qvu3D0aN962F"
   },
   "source": [
    "Hay una infinidad de bibliotecas o librerías dando vueltas por internet. Muchas veces el problema que queremos solucionar se reduce simplemente a encontrar la librería que tenga la funcionalidad correcta.\n",
    "\n",
    "Ahora continuaremos usando una muy utilizada en nuestro ámbito, la querídisima NumPy."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Z_Zz58m6962G"
   },
   "source": [
    "## _NumPy_ : vectores, matrices y tablas de datos\n",
    "\n",
    "NumPy (NUMeric PYthon) es **LA** biblioteca para operar sobre vectores de números. Además de contener un nuevo [tipo de dato](http://docs.scipy.org/doc/numpy/reference/arrays.ndarray.html) que nos va a ser muy útil para representar vectores y matrices, nos provee de un arsenal de [funciones de todo tipo](https://docs.scipy.org/doc/numpy/reference/routines.html).\n",
    "\n",
    "Vamos a empezar por importar la bliblioteca _numpy_. La sintaxis típica de eso era `import biblio as nombre`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "id": "ejBOu9HQ962H"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "El numero e = 2.718281828459045\n",
      "O el numero Pi = 3.141592653589793\n"
     ]
    }
   ],
   "source": [
    "import numpy as np  # con eso voy a poder acceder a las funciones de numpy a través de np.función()\n",
    "\n",
    "# Por ejemplo\n",
    "print(f\"El numero e = {np.e}\")\n",
    "print(f\"O el numero Pi = {np.pi}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "id": "8BjIa881S-i_"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.2246467991473532e-16\n"
     ]
    }
   ],
   "source": [
    "# Podemos calcular senos y cosenos de numeros igual que con math!\n",
    "print(np.sin(np.pi))  # casi cero! guarda con los floats!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "lSksN2iI962J"
   },
   "source": [
    "Todo eso está muy bien, pero lo importante de _numpy_ son los arrays numéricos, que van a ser como una lista de números pero con muchos esteroides. Los arrays numéricos nos van a servir para representar vectores (el objeto matemático de \"la tira de números\", no el físico) o columnas/tablas de datos (el objeto oriyinezco o de laboratorio).\n",
    "\n",
    "> (Ojo, los arrays no son vectores, aunque pueden comportarse como tales en muchos sentidos)\n",
    "\n",
    "La idea es que es parecido a una lista: son muchos números juntos en la misma variable y están indexados (los puedo llamar de a uno dando la posición dentro de la variable). La gran diferencia con las listas de Python es que los arrays de _numpy_ operan de la forma que todos queremos:\n",
    "1. Si sumamos o restamos dos arrays, se suman componente a componente.\n",
    "2. Si multiplicamos o dividimos dos arrays, se multiplican o dividen componente a componente.\n",
    "\n",
    "Veamos ejemplos usando la función `np.array` para crear arrays básicos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "id": "WJ71p4br962K"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ARRAYS:\n",
      "[1 2 3 4] + [5 6 7 8] =  [ 6  8 10 12]\n",
      "[1 2 3 4] * [5 6 7 8] = [ 5 12 21 32]\n"
     ]
    }
   ],
   "source": [
    "array_1 = np.array([1, 2, 3, 4])\n",
    "array_2 = np.array([5, 6, 7, 8])\n",
    "\n",
    "print(\"ARRAYS:\")\n",
    "print(f\"{array_1} + {array_2} =  {array_1 + array_2}\")\n",
    "print(f\"{array_1} * {array_2} = {array_1*array_2}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "EZaEuuZETcp7"
   },
   "source": [
    "En el caso de las listas esto era muy molesto"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "id": "rG7OAnYTTcLg"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LISTAS:\n",
      "[5, 6, 7, 8] + [1, 2, 3, 4] = [1, 2, 3, 4, 5, 6, 7, 8]\n"
     ]
    }
   ],
   "source": [
    "lista_1 = [1, 2, 3, 4]\n",
    "lista_2 = [5, 6, 7, 8]\n",
    "\n",
    "print(\"LISTAS:\")\n",
    "print(f\"{lista_1} + {lista_2} = {lista_1 + lista_2}\")  # sumar concatena\n",
    "# print(lista_1 * lista_2) # esto ni siquiera se puede hacer!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "a5yhuml3962L"
   },
   "source": [
    "Y al igual que con las listas, uno puede acceder a elementos específicos de un array con su índice:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "id": "RmKdobbT962M"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 2 3 4\n",
      "8\n"
     ]
    }
   ],
   "source": [
    "print(array_1[0], array_1[1], array_1[2], array_1[3])\n",
    "\n",
    "# Y más o menos vale todo lo que valía con listas\n",
    "print(array_2[-1])  # agarro al último elemento del array_2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "_95ieRhV962M"
   },
   "source": [
    "También podemos iterar sobre ellos con _for_ , de las mismas formas que habíamos visto para iterar listas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "id": "bcLrdFKg962N"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "array_1:\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "\n",
      "array_2:\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n"
     ]
    }
   ],
   "source": [
    "# Aca itero sobre los ELEMENTOS de array_1\n",
    "print(\"array_1:\")\n",
    "for num in array_1:\n",
    "    print(num)\n",
    "\n",
    "print()\n",
    "\n",
    "# Aca itero sobre los INDICES de array_2\n",
    "print(\"array_2:\")\n",
    "for j in range(len(array_2)):\n",
    "    print(array_2[j])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "vOQhszEc962N"
   },
   "source": [
    "#### Arrays de dos dimensiones\n",
    "\n",
    "Para crear *arrays* de dos dimensiones (o más), podemos aplicar la función `np.array` sobre una *lista de listas*:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "id": "Y7rWNeSB962O"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2 3]\n",
      " [4 5 6]\n",
      " [7 8 9]]\n"
     ]
    }
   ],
   "source": [
    "# Cada lista corresponde a una fila de la matriz\n",
    "\n",
    "M = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])\n",
    "\n",
    "print(M)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "E9IC_cd3gn2O"
   },
   "source": [
    "Aca hacer `M[0]` dara la primer FILA de la matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "id": "OHdX7Lt5gqBE"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3]\n"
     ]
    }
   ],
   "source": [
    "print(M[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "XPwPCK3TgxUF"
   },
   "source": [
    "Si queremos sacar la primer componente habra que hacer `M[0, 0]`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "id": "OWesiGfdgx12"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    }
   ],
   "source": [
    "print(M[0, 0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "c5CUGdHb962P"
   },
   "source": [
    "Para facilitar la vida del usuario _numpy_ viene con un montón de rutinas de creación de arrays típicos. En particular, arrays con cierta cantidad de elementos entre dos números (muy útil para crear dominios para gráficos).\n",
    "\n",
    "Veamos ejemplos de esos:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "id": "bUQe_D5K962P"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Numero de puntos fijo:\n",
      "[ 0.          1.11111111  2.22222222  3.33333333  4.44444444  5.55555556\n",
      "  6.66666667  7.77777778  8.88888889 10.        ]\n"
     ]
    }
   ],
   "source": [
    "# N = 10 puntos en el rango [0, 1] con 1/(N-1) de espaciamiento\n",
    "\n",
    "equi_linspace = np.linspace(0, 10, 10) # Probar cambiar a N = 11 puntos\n",
    "\n",
    "print(f'Numero de puntos fijo:\\n{equi_linspace}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "id": "BPjEtNLzhHjz"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Paso entre puntos fijo:\n",
      "[0.  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9]\n"
     ]
    }
   ],
   "source": [
    "#  Elijo el paso entre [0, 1), lo que me da\n",
    "#  {0, paso, 2*paso, ... n*paso} siempre que n*paso<1\n",
    "\n",
    "equi_arange = np.arange(0, 1, 0.1)\n",
    "\n",
    "print(f'Paso entre puntos fijo:\\n{equi_arange}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "UCsbhv9z962Q"
   },
   "source": [
    "Los arrays tienen ciertas propiedades como su _shape_ (de cuánto por cuánto) y el _dtype_ (qué tipo de cosas tiene adentro). Podemos acceder a estos datos de la siguiente manera:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "id": "grSCuJxV962Q"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "float64\n"
     ]
    }
   ],
   "source": [
    "# Array de 1000 elementos\n",
    "x = np.linspace(0, 10, 1000)\n",
    "\n",
    "# ¿De qué tipos son los elementos de x?\n",
    "print(x.dtype)  # Ojo, sin paréntesis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "id": "kCMWPo-gku6p"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2, 3)\n"
     ]
    }
   ],
   "source": [
    "# Matriz llena de 0 de 2 x 3\n",
    "ceros = np.array([[0,0,0],\n",
    "                  [0,0,0]])\n",
    "\n",
    "# De qué tamaño es la matriz\n",
    "print(ceros.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Ccs3GpRG962T"
   },
   "source": [
    "---\n",
    "\n",
    "### Ejercicio 0 (10 minutos)\n",
    "\n",
    "Vamos a crear los valores de tiempo y posición que uno espera para una caida libre. Para esto, vamos a necesitar un array de valores 10 equiespaciados para el tiempo $t$, desde 0 hasta 3 segundos, y luego obtener la posición en metros mediante la ecuación:\n",
    "\n",
    "$$y(t) = y_0 - \\frac{g}{2}t^2$$\n",
    "\n",
    "Donde asumimos velocidad inicial nula, $g = 9.81 \\mathrm{\\frac{m}{s^2}}$ e $y_0 = 100\\; \\mathrm{m}$. Llamar las variables de tiempo $t$ e $y$ como ```t_teorico``` e ```y_teorico``` respectivamente.\n",
    "\n",
    "Mas adelante compararemos estos valores con otros medidos en el laboratorio.\n",
    "\n",
    "**Recordar que podemos aplicar operaciones matemáticas a los _arrays_**\n",
    "\n",
    "---\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### *Referencia de funciones de Numpy*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "phT_hxAsjEcj"
   },
   "source": [
    "Hay un montón más de funciones muy utiles para trabajar con vectores. Aca les dejamos un resumen de las que consideramos las más importantes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Array original: [1 3 1 5]\n",
      "\n",
      "Suma: 10\n",
      "\n",
      "Producto: 15\n",
      "\n",
      "Promedio: 2.5\n",
      "\n",
      "Desviación estándar: 1.66\n",
      "\n",
      "Raíces cuadradas: [1.         1.73205081 1.         2.23606798]\n",
      "\n",
      "Producto cruz: [1 0 0] x [0 1 0] = [0 0 1]\n",
      "\n",
      "Producto punto: [1 2 3].[4 5 6] = 32\n",
      "\n",
      "Norma del vector [3. 4.] = 5.0\n",
      "\n",
      "Array de 5 números aleatorios entre 2 a 7: [4.28678539 6.48422374 6.36194969 6.08132769 5.13378536]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Array de números positivos\n",
    "array = np.array([1, 3, 1, 5])\n",
    "print(f\"Array original: {array}\\n\")\n",
    "\n",
    "# Sumo los elementos\n",
    "suma = np.sum(array)\n",
    "print(f\"Suma: {suma}\\n\")\n",
    "\n",
    "# Los multiplico\n",
    "producto = np.prod(array)\n",
    "print(f\"Producto: {producto}\\n\")\n",
    "\n",
    "# Promedio\n",
    "mean = np.mean(array)\n",
    "print(f\"Promedio: {mean}\\n\")\n",
    "\n",
    "# Desviación estandar\n",
    "std = np.std(array)\n",
    "print(f\"Desviación estándar: {std:.2f}\\n\")  # El \":.2f\" es para que muestre solo dos dígitos despues de la coma\n",
    "\n",
    "# Raíz de cada elemento\n",
    "raices = np.sqrt(array)\n",
    "print(f\"Raíces cuadradas: {raices}\\n\")\n",
    "\n",
    "# Producto vectorial\n",
    "e1 = np.array([1, 0, 0])\n",
    "e2 = np.array([0, 1, 0])\n",
    "e3 = np.cross(e1, e2)\n",
    "print(f\"Producto cruz: {e1} x {e2} = {e3}\\n\")\n",
    "\n",
    "# Producto escalar\n",
    "vector_a = np.array([1, 2, 3])\n",
    "vector_b = np.array([4, 5, 6])\n",
    "resultado = np.dot(vector_a, vector_b)\n",
    "print(f\"Producto punto: {vector_a}.{vector_b} = {resultado}\\n\")\n",
    "\n",
    "# Norma\n",
    "pitagoras = np.array([3., 4.])  \n",
    "norma = np.linalg.norm(pitagoras)  \n",
    "print(f\"Norma del vector {pitagoras} = {norma}\\n\")\n",
    "\n",
    "# Array de 5 números aleatorios entre 2 y 7\n",
    "random_array = np.random.rand(5)    # Esto me genera numeros aleatorios entre 0 y 1\n",
    "print(f\"Array de 5 números aleatorios entre 2 a 7: {random_array * 5 + 2}\\n\")\n",
    "                                    # Al multiplicar por 5 y sumar 2 los paso entre 2 y 7 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### *Creación de matrices de forma práctica*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "id": "UFnRtdHb962P"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matriz identidad:\n",
      "[[1. 0. 0.]\n",
      " [0. 1. 0.]\n",
      " [0. 0. 1.]]\n",
      "\n",
      "Matriz de ceros:\n",
      "[[0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]]\n",
      "\n",
      "Matriz de unos:\n",
      "[[1. 1. 1.]\n",
      " [1. 1. 1.]]\n",
      "\n",
      "Matriz llena de 42:\n",
      "[[42 42 42 42]\n",
      " [42 42 42 42]\n",
      " [42 42 42 42]]\n",
      "\n",
      "Identidad corrida:\n",
      "[[0. 1. 0. 0. 0.]\n",
      " [0. 0. 1. 0. 0.]\n",
      " [0. 0. 0. 1. 0.]\n",
      " [0. 0. 0. 0. 1.]\n",
      " [0. 0. 0. 0. 0.]]\n",
      "\n",
      "Matriz con diagonal cualquiera:\n",
      "[[1 0 0 0]\n",
      " [0 2 0 0]\n",
      " [0 0 3 0]\n",
      " [0 0 0 4]]\n",
      "\n",
      "Full en 2x6:\n",
      "[[42 42 42 42 42 42]\n",
      " [42 42 42 42 42 42]]\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Matriz identidad de 3x3\n",
    "identidad = np.identity(3)\n",
    "print(f'Matriz identidad:\\n{identidad}')\n",
    "print()\n",
    "\n",
    "# Matriz de todos 0 de 4x4\n",
    "ceros = np.zeros((4, 4))\n",
    "print(f'Matriz de ceros:\\n{ceros}')\n",
    "print()\n",
    "\n",
    "# Matriz de todos 1 de 2x3\n",
    "unos = np.ones((2, 3))\n",
    "print(f'Matriz de unos:\\n{unos}')\n",
    "print()\n",
    "\n",
    "# Matrix llena con 42 de 3x4\n",
    "full = np.full((3, 4), 42)\n",
    "print(f'Matriz llena de 42:\\n{full}')\n",
    "print()\n",
    "\n",
    "# Matriz con diagonal corrida de 5x5\n",
    "ojos = np.eye(5, k=1)\n",
    "print(f'Identidad corrida:\\n{ojos}')\n",
    "print()\n",
    "\n",
    "# Matriz con la diagonal que yo le doy\n",
    "diagonal = np.diag([1, 2, 3, 4])\n",
    "print(f'Matriz con diagonal cualquiera:\\n{diagonal}')\n",
    "print()\n",
    "\n",
    "# Convertimos a full a una matriz de 2x6\n",
    "convertida = full.reshape(2, 6)\n",
    "print(f\"Full en 2x6:\\n{convertida}\\n\")\n",
    "print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### *Operaciones con matrices*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "matriz:\n",
      "[[ 1  2]\n",
      " [-1  0]]\n",
      "\n",
      "matriz.T para su transpuesta:\n",
      "[[ 1 -1]\n",
      " [ 2  0]]\n",
      "\n",
      "np.linalg.inv(matriz) para su inversa:\n",
      "[[ 0.  -1. ]\n",
      " [ 0.5  0.5]]\n",
      "\n",
      "np.linalg.det(matriz) para su determinante: 2.0\n",
      "\n",
      "np.diag(matriz) para su diagonal: [1 0]\n",
      "\n",
      "np.linalg.eig(matriz) para\n",
      "sus autovalores: [0.5+1.32287566j 0.5-1.32287566j]\n",
      "y autovectores:\n",
      "[[ 0.81649658+0.j          0.81649658-0.j        ]\n",
      " [-0.20412415+0.54006172j -0.20412415-0.54006172j]]\n",
      "\n",
      "Producto matricial AB = C\n",
      "A =\n",
      "[[1 2 3]\n",
      " [4 5 6]]\n",
      "B =\n",
      "[[ 7  8]\n",
      " [ 9 10]\n",
      " [11 12]]\n",
      "C =\n",
      "[[ 58  64]\n",
      " [139 154]]\n",
      "\n",
      "Solución del sistema Ax=b con\n",
      "A = \n",
      "[[ 1  2]\n",
      " [-1  0]]\n",
      "b = [9 8]\n",
      "x = [-8.   8.5]\n"
     ]
    }
   ],
   "source": [
    "# Transpuesta (3x2)  \n",
    "matriz = np.array([[1, 2], \n",
    "                   [-1, 0]]) \n",
    "\n",
    "print(f\"matriz:\\n{matriz}\\n\")\n",
    "\n",
    "transpuesta = matriz.T  \n",
    "print(f\"matriz.T para su transpuesta:\\n{transpuesta:}\\n\")  \n",
    "\n",
    "# Matrix inversa\n",
    "inversa = np.linalg.inv(matriz)  \n",
    "print(f\"np.linalg.inv(matriz) para su inversa:\\n{inversa}\\n\")  \n",
    "\n",
    "# Determinante\n",
    "determinante = np.linalg.det(matriz)  \n",
    "print(f\"np.linalg.det(matriz) para su determinante: {determinante:.1f}\\n\")\n",
    "\n",
    "# Saco la diagonal de una matriz\n",
    "diagnal = np.diag(matriz)  \n",
    "print(f\"np.diag(matriz) para su diagonal: {diagnal}\\n\")\n",
    "\n",
    "# Autovalores y autovectores\n",
    "autovalores, autovectores = np.linalg.eig(matriz)\n",
    "print(\"np.linalg.eig(matriz) para\")\n",
    "print(f\"sus autovalores: {autovalores}\")  \n",
    "print(f\"y autovectores:\\n{autovectores}\\n\")  \n",
    "\n",
    "# Producto matricial A.B = C\n",
    "print(\"Producto matricial AB = C\")\n",
    "A = np.array([[1, 2, 3], \n",
    "              [4, 5, 6]])\n",
    "\n",
    "B = np.array([[7,   8], \n",
    "              [9,  10], \n",
    "              [11, 12]])  \n",
    "C = A @ B\n",
    "print(f\"A =\\n{A}\")\n",
    "print(f\"B =\\n{B}\")\n",
    "print(f\"C =\\n{C}\\n\")\n",
    "\n",
    "# Resolucion de una ecaución A.x = b\n",
    "A = matriz\n",
    "b = np.array([9, 8])  \n",
    "solucion = np.linalg.solve(A, b)  \n",
    "print(f\"Solución del sistema Ax=b con\")\n",
    "print(f\"A = \\n{A}\")\n",
    "print(f\"b = {b}\")\n",
    "print(f\"x = {solucion}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "6E7_LMjRqycH"
   },
   "source": [
    "## Llevando los datos a Python\n",
    "Muchas veces estamos acostumbrados a guardar los datos en hojas de Excel o en las Hoja de Cálculo de Drive. Python puede leer estas hojas utilizando las librerías adecuadas, pero es más sencillo, y es mejor práctica, exportar estos archivos en CSV para luego leerlos desde ahí.\n",
    "\n",
    "### Por qué CSV\n",
    "* El formato **CSV (Comma Separated Values)** es abierto y un estándar a la hora de guardar datos de tipo fila o columna. Guardar los datos en Excel o Drive no está mal, pero se dificulta a la hora de pasarle los archivos a un/a colega, los CSV los puede abrir cualquiera! Inclusive, se pueden abrir Excel y Drive si se busca visualizarlo mejor.\n",
    "* Con pocos datos no hay problemas de _lag_ o *crasheos*, pero si son muchos datos: _\"Microsoft Excel dejó de responder\"_ .$^1$\n",
    "\n",
    "\n",
    "Acá una imagen de cómo descargar los archivos de Drive en CSV y de cómo se ven una vez en la compu. Es solo un archivo de texto con valores separados con comas, nada místico.\n",
    "\n",
    "![](fig/export_drive_calc_to_csv.gif)\n",
    "\n",
    "$\\scriptsize\\text{1. Para archivos muchos muuuchos datos inclusive los CSV se pueden quedar corto, y para estos casos existen formatos específicos que dependen de la naturaleza de los datos.}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "KmP_7wBqqycI"
   },
   "source": [
    "### `np.loadtxt`\n",
    "\n",
    "Una vez tenemos el archivo que descargamos podemos leerlo desde Python utilizando numpy. En este caso, la linea es\n",
    "```python\n",
    "data = np.loadtxt('nombre_del_archivo.csv', delimiter=',', skiprows=1, unpack=True)\n",
    "```\n",
    "\n",
    "Desglosemos esto por argumentos:\n",
    "1. El primer argumento es ubicación del archivo con la ruta respecto del archivo de Python. En este caso tenemos ambos archivos en la misma carpeta por lo que es solo el nombre.\n",
    "2. El segundo argumento, _delimiter_, recibe un _string_ que le indica a Python cómo están separados los valores en nuestro archivo. En este caso es por comas porque son archivos CSV.\n",
    "3. El tercer argumento es más opcional, y nos permite evitar que Python lea algunas lineas del archivo. En nuestro caso pusimos *1* ya que queremos evitar que lea la primera linea, que dice _\"VAR 1, VAR 2\"_.\n",
    "4. Por qué `unpack=True`\n",
    "\n",
    "    `np.loadtxt()` por defecto te da los valores exactamente como están en el CSV, por lo que en este caso nos daría 2 columnas de datos con 20 filas. Utilizando `unpack=True` trasponemos los datos para pasar las columnas a filas, de modo que la primera fila (`data[0]`) sean los datos de _VAR 1_ y la segunda fila (`data[1]`) sean los valores de _VAR 2_. Acá el código utilizando `unpack=True` y sin utilizarlo\n",
    "    \n",
    "    También podríamos importarlo sin usar el `unpack=True` y luego usar `data = np.transpose(data)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "id": "NORDN2qbqycI"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Data sin unpack:\n",
      " [[ 0.    1.93  1.  ]\n",
      " [ 1.58  1.67  1.  ]\n",
      " [ 3.16  1.3   1.  ]\n",
      " [ 4.74  0.63  1.  ]\n",
      " [ 6.32  1.26  1.  ]\n",
      " [ 7.89  2.38  1.  ]\n",
      " [ 9.47  2.91  1.  ]\n",
      " [11.05  2.36  1.  ]\n",
      " [12.63  3.93  1.  ]\n",
      " [14.21  4.8   1.  ]\n",
      " [15.79  4.83  1.  ]\n",
      " [17.37  5.17  1.  ]\n",
      " [18.95  6.21  1.  ]\n",
      " [20.53  7.94  1.  ]\n",
      " [22.11  9.12  1.  ]\n",
      " [23.68 11.09  1.  ]\n",
      " [25.26 12.57  1.  ]\n",
      " [26.84 14.28  1.  ]\n",
      " [28.42 17.1   1.  ]\n",
      " [30.   20.56  1.  ]]\n",
      "Primera columna:\n",
      "[0.   1.93 1.  ]\n"
     ]
    }
   ],
   "source": [
    "data = np.loadtxt('data_exp.csv', delimiter=',', skiprows=1)\n",
    "\n",
    "print(f\"Data sin unpack:\\n {data}\")\n",
    "\n",
    "print(f'Primera columna:\\n{data[0]}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "id": "gsqqUxYSqycJ"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Data con unpack:\n",
      " [[ 0.    1.58  3.16  4.74  6.32  7.89  9.47 11.05 12.63 14.21 15.79 17.37\n",
      "  18.95 20.53 22.11 23.68 25.26 26.84 28.42 30.  ]\n",
      " [ 1.93  1.67  1.3   0.63  1.26  2.38  2.91  2.36  3.93  4.8   4.83  5.17\n",
      "   6.21  7.94  9.12 11.09 12.57 14.28 17.1  20.56]\n",
      " [ 1.    1.    1.    1.    1.    1.    1.    1.    1.    1.    1.    1.\n",
      "   1.    1.    1.    1.    1.    1.    1.    1.  ]]\n",
      "\n",
      "Primera columna:\n",
      "[ 0.    1.58  3.16  4.74  6.32  7.89  9.47 11.05 12.63 14.21 15.79 17.37\n",
      " 18.95 20.53 22.11 23.68 25.26 26.84 28.42 30.  ]\n"
     ]
    }
   ],
   "source": [
    "data = np.loadtxt('data_exp.csv', delimiter=',', skiprows=1, unpack=True)\n",
    "\n",
    "print(f\"Data con unpack:\\n {data}\\n\")\n",
    "\n",
    "print(f'Primera columna:\\n{data[0]}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "uYoXx7Tc962T"
   },
   "source": [
    "---\n",
    "\n",
    "### Ejercicio 1 (5 minutos)\n",
    "\n",
    "Ahora vamos a cargar los datos guardados en el laboratorio, utilizando un .csv y las funcionalidades de Numpy. Guardar el tiempo, la posición y su error en tres variables ```t_labo```, ```y_labo``` y ```err_y_labo```.\n",
    "\n",
    "Para cargar el archivo se pueden seguir los siguientes pasos:\n",
    "1. Descargar el archivo en este [link](https://raw.githubusercontent.com/fifabsas/talleresfifabsas/master/python/2_Numerico/data_caida_libre.csv). Pueden hacerlo con click derecho -> \"Guardar como...\"\n",
    "2. Importen el archivo data_caida_libre.csv a Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "b3UEu1FY962T"
   },
   "source": [
    "---\n",
    "## Graficar funciones"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "bCKr_oN7962U"
   },
   "source": [
    "A lo largo de nuestras carreras, y de la vida, nos encontramos con información que queremos **graficar**, como por ejemplo la posición en el tiempo de la pelota que cae. Vamos a ver que con la ayuda de la biblioteca [`matplotlib`](https://matplotlib.org/) esto no es nada complicado.\n",
    "\n",
    "Esta librería es muy grande, por lo que tiene divididas sus funciones en distintos módulos. Para lo que vamos a ver en esta segunda parte nos alcanza con la sublibrería ```pyplot```. Una de las formas de importar esta librería es:\n",
    "```python\n",
    "import matplotlib.pyplot as plt\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Yz7M358E962U"
   },
   "source": [
    "Podemos usar esta librería en conjunto con ```numpy``` para graficar las funciones que querramos.\n",
    "\n",
    "Veamos un ejemplo, grafiquemos la función $f(x) = \\sin(x)\\sin(20x)$ entre $0$ y $2\\pi$ (no tienen por qué entender la función, es solo el logo de [Arctic Monkeys](https://qph.fs.quoracdn.net/main-qimg-69d69b537bb5e7e3f21e44c36781a10d))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "id": "Ehsyy74X962V"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Definimos la función\n",
    "def f(x):\n",
    "    return np.sin(x)*np.sin(20*x)\n",
    "\n",
    "# Definimos el dominio y la imagen\n",
    "x = np.linspace(0, 2*np.pi, 500)\n",
    "y = f(x)\n",
    "\n",
    "# Graficamos la función\n",
    "plt.plot(x, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "wVzheD-v962V"
   },
   "source": [
    "Desglosemos el código que acabamos de escribir:\n",
    "* Primero escribimos la función que queremos graficar.\n",
    "* Luego, definimos nuestro dominio `x` y nuestra imagen `y`.\n",
    "* Y por último usamos la función de `plot` de `matplotlib.pyplot` para graficar `y` en función de `x`.\n",
    "\n",
    "**Aclaración 1: plt.show():**\n",
    "Si bien esta linea no es siempre necesaria en los notebooks (como google Colab), su propósito es \"cerrar\" la figura y mostrarla.\n",
    "\n",
    "**Aclaración 2:** `y` no es una función. Sino que es un _array_ que contiene los números que resultan de aplicarle `f` a cada uno de los valores de `x`. Lo que vemos arriba parece ser una _función continua_ pero en realidad es un conjunto de punto unidos con una línea. Para visualizar mejor esto podemos hacer un gráfico que muestre explícitamente los puntos que forman el gráfico:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "id": "wV8EmrWB962W"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y, '.-')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "UK7dME4T962W"
   },
   "source": [
    "#### Qué hace plt.plot()?\n",
    "Esta función que parece mágica lo único que hace es tomar los vectores que le damos como inputs y graficar un punto en cada par de coordenadas $(x,y)$. Además, por defecto une estos puntos con lineas rectas. Por lo tanto, para que la función pueda hacer su trabajo, es necesario que los _array_ ```x``` e ```y``` tengan la misma longitud. Para dejar claro este concepto veamos un ejemplo con pocos puntos escritos a mano:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "id": "X3vFYJl1962X"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "coords_en_x = np.array([0, 2, 6, 8,  10])\n",
    "coords_en_y = np.array([2, 4, 6, 14, 14])\n",
    "\n",
    "plt.plot(coords_en_x, coords_en_y, 'o:r')\n",
    "plt.grid()  # Esto me deja poner una grilla detrás!\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "lglTUHTn962X"
   },
   "source": [
    "Vemos que los puntos que se grafican son los $(x,y)$ = $\\{(0,2);\\,(2,4);\\,(6,6);\\,(8,14);\\,(10,14)\\}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "JIYzGyRw962X"
   },
   "source": [
    "### Dar formato y estética a los gráficos\n",
    "\n",
    "En los gráficos anteriores cuando usamos `plt.plot` agregamos un término opcional para cambiar el color y la forma en la que se muestran los puntos que graficamos. Si usamos `help(plt.plot)` vemos que este argumento opcional es el _[fmt]_ y que toma distintos _strings_ con los que se puede cambiar la forma en que se ve el gráfico. La estructura general es\n",
    "```python\n",
    "fmt = '[color][marker][line]'\n",
    "```\n",
    "donde _marker_ hace referencia a la forma de los puntitos y _line_ hace referencia a la forma de la linea.\n",
    "\n",
    "Los _strings_ válidos son un montón y los pueden ver en la documentación usando el _help_ o en la [documentación online](https://matplotlib.org/3.2.1/api/_as_gen/matplotlib.pyplot.plot.html) de la función.\n",
    "\n",
    "Acá dejamos algunas de las opciones para que se den una idea:\n",
    "* **color:** 'r' (rojo), 'b' (azul), 'g' (verde), 'm' (magenta), etc\n",
    "* **marker:** '.' (puntito chiquito), 'o' (punto grande), '^' (triángulo), '*' (estrella), etc\n",
    "* **line:** '-' (sólida), '--' (de a rayas), ':' (de a puntos)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "jBpAdMwPq28m"
   },
   "source": [
    "<img src=\"https://matplotlib.org/stable/_images/sphx_glr_named_colors_003_2_00x.png\" alt=\"colores_matplotlib\" width=\"600\" height=\"600\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "EgQ5ky3bihUg"
   },
   "source": [
    "### Título, labels y grid\n",
    "Veamos también algunas funciones que nos permiten agregar información a la figura sobre la que estamos trabajando. Veamos un ejemplo con la función de los [Arctic Monkeys](https://qph.fs.quoracdn.net/main-qimg-69d69b537bb5e7e3f21e44c36781a10d)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "z2-xCQeY962Y"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Definimos la función\n",
    "def f(x):\n",
    "    return np.sin(x)*np.sin(20*x)\n",
    "\n",
    "# Definimos el dominio y la imagen\n",
    "x = np.linspace(0, 2*np.pi, 500)\n",
    "y = f(x)\n",
    "\n",
    "# Graficamos la función con linea sólida y le ponemos una etiqueta\n",
    "plt.plot(x, y, '-', label='Arctic Monkeys')\n",
    "\n",
    "# Agregamos título y etiquetamos los ejes\n",
    "plt.title('Logo de los Arctic Monkeys', fontsize=16)\n",
    "plt.xlabel('Eje de $\\hat x$')\n",
    "plt.ylabel('Eje de $\\hat y$')\n",
    "\n",
    "plt.grid()\n",
    "plt.legend(loc=\"upper right\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "dphh2LbZ962Y"
   },
   "source": [
    "La mayoría de las funciones son bastante descriptivas. Veamos solo algunas aclaraciones:\n",
    "* El _fontsize_ en el ```plt.title``` es un argumento opcional y también se puede utilizar en el ```plt.xlabel``` o ```plt.ylabel``` por ejemplo.\n",
    "* El ```plt.grid()``` agrega una grid si no exite y la elimina si existe. Si se quiere forzar a que aparezca se puede utilizar ```plt.grid(True)```\n",
    "* El ```plt.legend()``` es el que permite que se muestren los labels asociados a las lineas (en este caso es el \"Arctic Monkeys\"). Esta función tiene algunos parámetros opcionales que pueden probar como el _fontsize_ o el _loc_. (ver ```help(plt.legend)```)\n",
    "* Podemos usar $\\LaTeX$ en los labels!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ooQ8-irSJPmC"
   },
   "source": [
    "Aca abajo dejamos una figura con los nombres de las distintas partes de una figura para que tengan a mano a la hora de googlear como cambiar cada parte. (fuente: [este libro hermoso](https://www.labri.fr/perso/nrougier/scientific-visualization.html))\n",
    "\n",
    "<img src=\"https://pbs.twimg.com/media/Cr5jxB-UkAAmvBn?format=jpg&name=medium\" alt=\"Milanesa\" width=\"600\" height=\"600\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "edwV5lcH962Z"
   },
   "source": [
    "---\n",
    "### Ejercicio 2 (10 minutos)\n",
    "\n",
    "En la misma figura:\n",
    "* Graficar los datos cargados en las variables ```t_teorico``` e ```y_teorico```. Etiquetar los datos como 'Teorico'.\n",
    "* Graficar los datos cargados en las variables ```t_labo``` e ```y_labo```. Etiquetar los datos como 'Laboratorio'.\n",
    "* Agregar la leyenda, etiquetar los ejes y poner\n",
    "un título (pueden usar $\\LaTeX$ si conocen la syntaxis)\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "6QWAxhWX962Z"
   },
   "source": [
    "## Hacer ajustes\n",
    "\n",
    "Vamos a levantar nuevamente unos datos para graficarlos igual que lo hacíamos antes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "id": "4bUI5T2x962Z"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Importamos los datos\n",
    "data = np.loadtxt('data_exp.csv', delimiter=',', skiprows=1, unpack=True)\n",
    "\n",
    "# Los ponemos en variables\n",
    "tiempo = data[0]\n",
    "num_conejos = data[1]\n",
    "err_num_conejos = data[2]\n",
    "\n",
    "# O lo que es lo mismo\n",
    "tiempo, num_conejos, err_num_conejos = data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "id": "86bRsQNApOK9"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Graficamos los datos crudos\n",
    "plt.plot(tiempo, num_conejos, 'ok', label='Datos')\n",
    "\n",
    "# Labels, grilla, leyenda y show\n",
    "plt.xlabel(\"Tiempo\")\n",
    "plt.ylabel(\"Número de conejos\")\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "mgs3Wau4962a"
   },
   "source": [
    "Los datos parecen tener un comportamiento exponencial. Queremos ver que tan exponencial es su distribución realizando un ajuste. Realizamos un ajuste primero definiendo la función que queremos comparar a los datos, $f$, con los parametros libres que nos interesa determinar,\n",
    "$$\n",
    "\\text{variable dependiente} = f(\\text{variable independiente}, \\text{parametros a determinar}).\n",
    "$$\n",
    "\n",
    "En este caso, vamos a intentar con:\n",
    "$$\n",
    "f(t, A, C) = Ae^{Ct}\n",
    "$$\n",
    "\n",
    "Luego, para realizar un ajuste podemos usar la función ```curve_fit()``` que nos ofrece la librería/sublibrería ```scipy.optimize```. Veamos cómo funciona con un ejemplo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "id": "KtuTMK_vDXh5"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parámetros óptimos para A y C (popt): [0.97349008 0.10119234]\n",
      "\n",
      "Matriz de covariancia de popt (pcov):\n",
      "[[ 1.93987073e-02 -7.45513975e-04]\n",
      " [-7.45513975e-04  2.96163048e-05]]\n"
     ]
    }
   ],
   "source": [
    "# Importo la función desde la librería\n",
    "from scipy.optimize import curve_fit\n",
    "\n",
    "# Declaro la función con la que quiero ajustar con parámetros genéricos\n",
    "def f_ajuste(t, A, C):\n",
    "    exponencial = A*np.exp(C*t)\n",
    "    return exponencial\n",
    "\n",
    "# Utilizo curve_fit() para el ajuste\n",
    "popt, pcov = curve_fit(f_ajuste, tiempo, num_conejos, sigma=err_num_conejos, absolute_sigma=True)\n",
    "\n",
    "# Imprimo en pantalla los valores de popt y pcov\n",
    "print(f'Parámetros óptimos para A y C (popt): {popt}')\n",
    "print(f'\\nMatriz de covariancia de popt (pcov):\\n{pcov}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "id": "jPwdMZAGDoGW"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Graficamos los DATOS con el error asociado\n",
    "plt.errorbar(tiempo, num_conejos, yerr=err_num_conejos, fmt='ok', label='Datos',\n",
    "             capsize=2, capthick=1)\n",
    "\n",
    "\n",
    "# Graficamos el AJUSTE\n",
    "A, C = popt\n",
    "# Variables finas para evaluar la funcion en más puntos que los medidos\n",
    "x_ajuste = np.linspace(min(tiempo), max(tiempo), 1000)\n",
    "y_ajuste = f_ajuste(x_ajuste, A, C)\n",
    "\n",
    "plt.plot(x_ajuste, y_ajuste, '-r', label='Ajuste')\n",
    "\n",
    "\n",
    "# Labels, grilla, leyenda y show\n",
    "plt.xlabel(\"Tiempo\")\n",
    "plt.ylabel(\"Número de conejos\")\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "L0-YsLe1962a"
   },
   "source": [
    "##### Vemos que arriba la función recibe cinco inputs (3 obligatorios y 2 opcionales):\n",
    "* `f`: **El primer argumento es la función _modelo_ con la que queremos ajustar.**\n",
    "    \n",
    "    La función modelo tiene que tener como primer parámetro la variable independiente (que corresponde por ejemplo al eje $\\hat x$). Luego se usan los otros parámetros para poner las constantes que queremos hallar (en nuestro caso `A` y `C`).\n",
    "\n",
    "\n",
    "* `xdata, ydata`: **Los otros dos argumentos son nuestros datos**\n",
    "\n",
    "    Estos son los datos crudos, los que usamos para visualizarlos normalmente.\n",
    "    \n",
    "* `sigma`: **El error asociado a cada valor en** `ydata`\n",
    "    \n",
    "    Es un parámetro opcional, para que el ajuste considere el error en la variable $y$.\n",
    "\n",
    "* `absolute_sigma`: **Para que el ajuste nos devuelva los errores en términos absolutos** \n",
    "    \n",
    "    Es un parámetro opcional, para que el ajuste considere los errores como absolutos.\n",
    "\n",
    "\n",
    "##### Outputs de `curve_fit()`\n",
    "* `popt`: **Parámetros Óptimos (`array 1D` de numpy)**\n",
    "    \n",
    "    Vemos que `curve_fit()` nos devuelve como primer parámetro una lista con los valores óptimos para nuestro ajuste. En este caso son dos porque en la función modelo pusimos dos constantes (`A` y `C`). Estos valores vienen ordenados del mismo modo que están en la función modelo por lo que `popt[0]` es el `A` óptimo y `popt[1]` es el `C` óptimo.\n",
    "\n",
    "\n",
    "* `pcov`: **Covarianza de los Parámetros (`array 2D` de numpy)**\n",
    "    \n",
    "    Esta es la matriz de covarianza de los resultados que nos da `popt`. Esta matriz nos da una idea de cuál es el error de este ajuste y de cuán ligados están estos errores entre sí. No es el objetivo del curso dar una clase de estadísitica, pero si conocemos que las variables son independientes podemos obtener el error de nuestros parámetros de ajuste como la raíz cuadrada de la covarianza. Para este ejemplo sería\n",
    "    ```python\n",
    "    err_A = np.sqrt(pcov[0,0])\n",
    "    err_C = np.sqrt(pcov[1,1])\n",
    "    ```\n",
    "    o\n",
    "    ```python\n",
    "    err_A, err_C = np.sqrt(np.diag(pcov))\n",
    "    ```\n",
    "\n",
    "**Una cosita más:** En este caso pusimos `var_x_ajuste = var_x` al momento de graficar, lo que implica que nuestro grafico del ajuste tiene 20 puntos (los mismos que `var_x`), pero como conocemos la función podríamos hacer un linspace del estilo `np.linspace(min(var_x), max(var_x), 1000)` para tener una mejor densidad de puntos. Esto esta bueno para hacer que los gráficos se vean menos acartonados, pero SOLAMENTE se puede usar a la hora de graficar."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ITpYWJC3962b"
   },
   "source": [
    "#### Barras de error\n",
    "\n",
    "* Si queremos poner barras de error a nuestro gráfico podemos usar ```plt.errorbar()```, que funciona de forma muy similar a ```plt.plot()``` pero nos permite dar un array con los errores o un error constante para todos.\n",
    "\n",
    "#### Guardar un gráfico\n",
    "Una vez tenemos un gráfico podemos guardarlo en el mismo directorio donde tenemos el archivo con el que estamos trabajando utilizando la linea\n",
    "```python\n",
    "plt.savefig('nombre_del_archivo.png')\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "9RLsaOc1962b"
   },
   "source": [
    "---\n",
    "### Ejercicio 3 (15 minutos)\n",
    "\n",
    "Con los datos levantados en las variables ```t_labo``` e ```y_labo```, realizar el ajuste de la función:\n",
    "\n",
    "$$y(t) = a + b \\; t^2$$\n",
    "\n",
    "Donde $a = y_0$ y $b = -\\frac{g}{2}$.\n",
    "\n",
    "Agregar al gráfico del Ejercicio 3 este nuevo ajuste, junto con su label 'Ajuste'.\n",
    "\n",
    "Guardar la imagen, e imprimir la gravedad en pantalla con su error.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "37lw9cFC962d"
   },
   "source": [
    "### Acá termina nuestra clase.\n",
    "\n",
    "Si aún hay tiempo abajo tenemos armado algunos párrafos sobre distintas cosas piolas que podemos hacer. La elección esta en ustedes. (Si, se convirtió en un elija su propia aventura, no se la esperaba nadie esa)\n",
    "\n",
    "* Pandas y DataFrames\n",
    "* Histogramas\n",
    "* Sistemas de ecuaciones diferenciales\n",
    "* Algebra Lineal\n",
    "* Calculo Simbólico\n",
    "* Integración Numérica\n",
    "* Funciones Locas\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "HcgRMSPQ962d"
   },
   "source": [
    "---\n",
    "# Pandas y DataFrames\n",
    "\n",
    "[Pandas](https://pandas.pydata.org/) es una librería bastante utilizada para Análisis de Datos y tiene [demasiadas](https://pandas.pydata.org/docs/user_guide/index.html) cosas disponibles, demasiadas. Aca en el curso no vamos a cubrir casi nada, sólo veremos algunas cosas.\n",
    "\n",
    "Pandas, tal como NumPy y SymPy, trae un nuevo tipo de dato muy genial, los DataFrames. Recomendado es el [tutorial](https://pandas.pydata.org/docs/getting_started/index.html) de 10 minutos que aporta la misma página de Pandas, en los que hace un paneo sobre las cosas básicas de la librería. Hay un [ejemplo práctico](https://github.com/fifabsas/talleresfifabsas/blob/master/python/Extras/Pandas_ejemplo.ipynb) hecho por la FIFA en el que se trabaja un poco los datos de inscripción de una jornada anterior del cursito este.\n",
    "\n",
    "Los DataFrames, el nuevo tipo de dato introducido, son básicamente tablas de datos donde cada columna tiene un nombre descriptivo. Podemos operar con las columnas por su nombre, y también elegir filas como haciamos con arrays antes.\n",
    "\n",
    "\n",
    "Vamos a trabajar con un csv que pueden descargar de nuestro repositorio:\n",
    "\n",
    "[Datos de los jugadores](https://github.com/fifabsas/talleresfifabsas/blob/master/python/2_Numerico/datos_jugadores.csv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "id": "dWDVUYHiscn9"
   },
   "outputs": [],
   "source": [
    "# Importamos pandas con un sobrenombre, como haciamos con numpy\n",
    "\n",
    "import pandas as pd\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "id": "MLSXXan1sik_"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        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>Equipo</th>\n",
       "      <th>Puesto</th>\n",
       "      <th>Jugador</th>\n",
       "      <th>Edad</th>\n",
       "      <th>Nacimiento</th>\n",
       "      <th>dia_mes</th>\n",
       "      <th>nro_mes</th>\n",
       "      <th>año</th>\n",
       "      <th>Altura_cm</th>\n",
       "      <th>Ciudad_nac</th>\n",
       "      <th>Pais_nac</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Tigre</td>\n",
       "      <td>MED</td>\n",
       "      <td>Aaron Molinas</td>\n",
       "      <td>22</td>\n",
       "      <td>8/2/2000</td>\n",
       "      <td>02-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>2000</td>\n",
       "      <td>175.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Argentina</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Banfield</td>\n",
       "      <td>DEF</td>\n",
       "      <td>Aarón Quirós</td>\n",
       "      <td>21</td>\n",
       "      <td>10/31/2001</td>\n",
       "      <td>31-oct</td>\n",
       "      <td>10</td>\n",
       "      <td>2001</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Argentina</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Tigre</td>\n",
       "      <td>DEF</td>\n",
       "      <td>Abel Luciatti</td>\n",
       "      <td>30</td>\n",
       "      <td>2/18/1993</td>\n",
       "      <td>18-feb</td>\n",
       "      <td>2</td>\n",
       "      <td>1993</td>\n",
       "      <td>178.0</td>\n",
       "      <td>Morón</td>\n",
       "      <td>Argentina</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Velez</td>\n",
       "      <td>DEL</td>\n",
       "      <td>Abiel Osorio</td>\n",
       "      <td>20</td>\n",
       "      <td>6/13/2002</td>\n",
       "      <td>13-jun</td>\n",
       "      <td>6</td>\n",
       "      <td>2002</td>\n",
       "      <td>182.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Argentina</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>San Lorenzo</td>\n",
       "      <td>DEL</td>\n",
       "      <td>Adam Bareiro</td>\n",
       "      <td>26</td>\n",
       "      <td>7/26/1996</td>\n",
       "      <td>26-jul</td>\n",
       "      <td>7</td>\n",
       "      <td>1996</td>\n",
       "      <td>184.0</td>\n",
       "      <td>Asuncion</td>\n",
       "      <td>Paraguay</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>639</th>\n",
       "      <td>Atl Tucuman</td>\n",
       "      <td>DEF</td>\n",
       "      <td>Wilson Ibarrola</td>\n",
       "      <td>26</td>\n",
       "      <td>7/2/1996</td>\n",
       "      <td>02-jul</td>\n",
       "      <td>7</td>\n",
       "      <td>1996</td>\n",
       "      <td>172.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Paraguay</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>640</th>\n",
       "      <td>Sarmiento (J)</td>\n",
       "      <td>MED</td>\n",
       "      <td>Yair Arismendi</td>\n",
       "      <td>25</td>\n",
       "      <td>4/5/1998</td>\n",
       "      <td>05-abr</td>\n",
       "      <td>4</td>\n",
       "      <td>1998</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Argentina</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>641</th>\n",
       "      <td>Union</td>\n",
       "      <td>MED</td>\n",
       "      <td>Yeison Gordillo</td>\n",
       "      <td>30</td>\n",
       "      <td>6/25/1992</td>\n",
       "      <td>25-jun</td>\n",
       "      <td>6</td>\n",
       "      <td>1992</td>\n",
       "      <td>176.0</td>\n",
       "      <td>Miranda (Cauca)</td>\n",
       "      <td>Colombia</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>642</th>\n",
       "      <td>Atl Tucuman</td>\n",
       "      <td>DEF</td>\n",
       "      <td>Yonathan Cabral</td>\n",
       "      <td>30</td>\n",
       "      <td>5/10/1992</td>\n",
       "      <td>10-may</td>\n",
       "      <td>5</td>\n",
       "      <td>1992</td>\n",
       "      <td>188.0</td>\n",
       "      <td>Isidro Casanova</td>\n",
       "      <td>Argentina</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>643</th>\n",
       "      <td>Estudiantes (LP)</td>\n",
       "      <td>DEF</td>\n",
       "      <td>Zaid Romero</td>\n",
       "      <td>23</td>\n",
       "      <td>12/15/1999</td>\n",
       "      <td>15-dic</td>\n",
       "      <td>12</td>\n",
       "      <td>1999</td>\n",
       "      <td>193.0</td>\n",
       "      <td>Mendoza</td>\n",
       "      <td>Argentina</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>644 rows × 11 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "               Equipo Puesto          Jugador  Edad  Nacimiento dia_mes  \\\n",
       "0               Tigre    MED    Aaron Molinas    22    8/2/2000  02-ago   \n",
       "1            Banfield    DEF     Aarón Quirós    21  10/31/2001  31-oct   \n",
       "2               Tigre    DEF    Abel Luciatti    30   2/18/1993  18-feb   \n",
       "3               Velez    DEL     Abiel Osorio    20   6/13/2002  13-jun   \n",
       "4         San Lorenzo    DEL     Adam Bareiro    26   7/26/1996  26-jul   \n",
       "..                ...    ...              ...   ...         ...     ...   \n",
       "639       Atl Tucuman    DEF  Wilson Ibarrola    26    7/2/1996  02-jul   \n",
       "640     Sarmiento (J)    MED   Yair Arismendi    25    4/5/1998  05-abr   \n",
       "641             Union    MED  Yeison Gordillo    30   6/25/1992  25-jun   \n",
       "642       Atl Tucuman    DEF  Yonathan Cabral    30   5/10/1992  10-may   \n",
       "643  Estudiantes (LP)    DEF      Zaid Romero    23  12/15/1999  15-dic   \n",
       "\n",
       "     nro_mes   año  Altura_cm       Ciudad_nac   Pais_nac  \n",
       "0          8  2000      175.0              NaN  Argentina  \n",
       "1         10  2001        NaN              NaN  Argentina  \n",
       "2          2  1993      178.0            Morón  Argentina  \n",
       "3          6  2002      182.0              NaN  Argentina  \n",
       "4          7  1996      184.0         Asuncion   Paraguay  \n",
       "..       ...   ...        ...              ...        ...  \n",
       "639        7  1996      172.0              NaN   Paraguay  \n",
       "640        4  1998        NaN              NaN  Argentina  \n",
       "641        6  1992      176.0  Miranda (Cauca)   Colombia  \n",
       "642        5  1992      188.0  Isidro Casanova  Argentina  \n",
       "643       12  1999      193.0          Mendoza  Argentina  \n",
       "\n",
       "[644 rows x 11 columns]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Para cargar un csv usamos read_csv() de pandas.\n",
    "# El argumento es el nombre del archivo\n",
    "df = pd.read_csv('datos_jugadores.csv')\n",
    "\n",
    "# df es un \"DataFrame\", como si fuera una tabla de Excel cargada en Python.\n",
    "\n",
    "display(df) # Display es como un \"print\" especial para cosas que no son texto."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "id": "MXZyvrqczLUs"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(644, 11)\n",
      "Index(['Equipo', 'Puesto', 'Jugador', 'Edad', 'Nacimiento', 'dia_mes',\n",
      "       'nro_mes', 'año', 'Altura_cm', 'Ciudad_nac', 'Pais_nac'],\n",
      "      dtype='object')\n"
     ]
    }
   ],
   "source": [
    "# Obtener cantidad de filas y columnas total:\n",
    "print(df.shape)\n",
    "\n",
    "# Obtener nombres de las columnas:\n",
    "print(df.columns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "pxc5IhQ4tN90"
   },
   "source": [
    "Nos gustaría operar de alguna manera con esta tabla, para hacer algun tipo de análisis de los datos.\n",
    "\n",
    "Preguntas posibles:\n",
    "- Cuál es la distribución de edad/altura/año de nacimiento?\n",
    "- Cuantos jugadores de cada País/Puesto/mes de nacimiento hay?\n",
    "- Hay dos jugadores que compartan cumpleaños en un mismo equipo?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "IQ7ZnQ6VwwaM"
   },
   "source": [
    "## Cuál es la distribución de edad?\n",
    "\n",
    "Para esta pregunta vamos a armar un histograma de los valores de edad."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "id": "JF5HB7TTw4xw"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Para seleccionar una columna usamos:\n",
    "altura = df['Altura_cm']\n",
    "\n",
    "altura.hist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "id": "pMGWoi9Xxd-y"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Dejemos un poco más lindo el gráfico\n",
    "\n",
    "altura.hist(rwidth=0.9, edgecolor='black', color='lightblue')\n",
    "\n",
    "# Label de los ejes\n",
    "plt.xlabel('Altura [cm]', fontsize=13)\n",
    "plt.ylabel('Ocurrencias', fontsize=13)\n",
    "\n",
    "# Apagamos la grid que viene por defecto y despues colocamos la nuestra\n",
    "plt.grid()\n",
    "plt.grid(ls='--', axis='y', color='gray')\n",
    "\n",
    "plt.title('Distribución de altura de los jugadores')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "3fjrpaOUx8ge"
   },
   "source": [
    "Como hacemos si queremos crear una columna nueva? Por ejemplo, el logaritmo de la altura?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "id": "63Qh-KE6x7T0"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df['Altura_log'] = np.log(df['Altura_cm'])\n",
    "\n",
    "# Dejemos un poco más lindo el gráfico\n",
    "df['Altura_log'].hist(rwidth=0.9, edgecolor='black', color='lightblue')\n",
    "\n",
    "# Label de los ejes\n",
    "plt.xlabel('log(Altura)', fontsize=13)\n",
    "plt.ylabel('Ocurrencias', fontsize=13)\n",
    "\n",
    "# Apagamos la grid que viene por defecto y despues colocamos la nuestra\n",
    "plt.grid()\n",
    "plt.grid(ls='--', axis='y', color='gray')\n",
    "\n",
    "plt.title('Distribución de altura de los jugadores')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "pJ_DNmFVu3hd"
   },
   "source": [
    "## Cuántos jugadores de cada pais hay?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "id": "q4KT0Q2Vu7_C"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pandas.core.groupby.generic.DataFrameGroupBy object at 0x7e3ddf482e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Podemos usar la función groupby de pandas para agrupar todas las filas\n",
    "# con el mismo país de nacimiento.\n",
    "\n",
    "df_gb = df.groupby('Pais_nac')\n",
    "\n",
    "display(df_gb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "zjKOnIczvLLc"
   },
   "source": [
    "Vemos que esto asi solo no nos dice absolutamente nada. Una vez que tenemos agrupado por una columna nuestro DataFrame, podemos hacer cálculos como el promedio, la suma de los valores, la cantidad de veces que aparece una fila con el valor que agrupamos, el máximo, etc. A estas se las conoce como funciones de agregación."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "id": "qqy0Cb1lvY1X"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pais_nac\n",
       "Argentina    544\n",
       "Chile          5\n",
       "Colombia      22\n",
       "Ecuador        3\n",
       "Espana         3\n",
       "Mexico         1\n",
       "Paraguay      28\n",
       "Peru           2\n",
       "Portugal       1\n",
       "Uruguay       33\n",
       "Venezuela      2\n",
       "Name: Equipo, dtype: int64"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Para contar la cantidad de filas seleccionamos una columna cualquiera y usamos 'count'.\n",
    "\n",
    "df_gb['Equipo'].count()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "id": "m7_DkU3AwdP4"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pais_nac\n",
       "Argentina    194.0\n",
       "Chile        180.0\n",
       "Colombia     190.0\n",
       "Ecuador      176.0\n",
       "Espana       192.0\n",
       "Mexico       178.0\n",
       "Paraguay     188.0\n",
       "Peru         185.0\n",
       "Portugal     176.0\n",
       "Uruguay      190.0\n",
       "Venezuela    186.0\n",
       "Name: Altura_cm, dtype: float64"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Si quisieramos el máximo de altura, por ejemplo:\n",
    "\n",
    "df_gb['Altura_cm'].max()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Smzezd51uyNC"
   },
   "source": [
    "## Hay dos jugadores que compartan cumpleaños en un mismo equipo?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "id": "y8nQrB--s_CL"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Equipo      dia_mes\n",
       "Argentinos  01-dic     1\n",
       "            02-feb     1\n",
       "            04-jul     1\n",
       "            07-nov     1\n",
       "            08-ago     1\n",
       "                      ..\n",
       "Velez       25-feb     1\n",
       "            26-jun     1\n",
       "            28-abr     1\n",
       "            30-ene     1\n",
       "            31-ene     1\n",
       "Name: Puesto, Length: 622, dtype: int64"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Para responder esto, podemos contar cuantas veces se repite\n",
    "# el mismo valor de \"Equipo\" y \"dia_mes\". Para hacer esto, podemos aprovechar\n",
    "# a usar devuelta el groupby, y contar cuantas veces está esa combinaciones\n",
    "# de valores\n",
    "\n",
    "df_gb = df.groupby(['Equipo', 'dia_mes'])['Puesto'].count()\n",
    "\n",
    "display(df_gb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "id": "T5RkU99ItxHE"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Equipo             dia_mes\n",
       "Argentinos         25-ene     2\n",
       "Atl Tucuman        10-may     2\n",
       "                   17-feb     2\n",
       "Banfield           01-feb     2\n",
       "Belgrano           29-ago     2\n",
       "Boca Juniors       04-jul     2\n",
       "                   22-feb     2\n",
       "                   23-jul     2\n",
       "                   24-abr     2\n",
       "Central Cba (SdE)  13-ene     2\n",
       "                   27-oct     2\n",
       "Colon              05-sep     2\n",
       "                   13-ene     2\n",
       "Def y Justicia     08-feb     2\n",
       "Estudiantes (LP)   29-mar     2\n",
       "Gimnasia (LP)      05-may     2\n",
       "Godoy Cruz         02-mar     2\n",
       "                   16-feb     2\n",
       "Lanus              22-mar     2\n",
       "River Plate        29-mar     2\n",
       "Tigre              07-feb     2\n",
       "Union              30-jul     2\n",
       "Name: Puesto, dtype: int64"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Ahora podemos filtrar usando esta sintaxis\n",
    "\n",
    "df_filtered = df_gb[df_gb > 1]\n",
    "\n",
    "display(df_filtered)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "id": "Hyd3CN5Ey4TH"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        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>Equipo</th>\n",
       "      <th>Puesto</th>\n",
       "      <th>Jugador</th>\n",
       "      <th>Edad</th>\n",
       "      <th>Nacimiento</th>\n",
       "      <th>dia_mes</th>\n",
       "      <th>nro_mes</th>\n",
       "      <th>año</th>\n",
       "      <th>Altura_cm</th>\n",
       "      <th>Ciudad_nac</th>\n",
       "      <th>Pais_nac</th>\n",
       "      <th>Altura_log</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Tigre</td>\n",
       "      <td>MED</td>\n",
       "      <td>Aaron Molinas</td>\n",
       "      <td>22</td>\n",
       "      <td>8/2/2000</td>\n",
       "      <td>02-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>2000</td>\n",
       "      <td>175.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.164786</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>67</th>\n",
       "      <td>Independiente</td>\n",
       "      <td>DEL</td>\n",
       "      <td>Braian Martínez</td>\n",
       "      <td>23</td>\n",
       "      <td>8/18/1999</td>\n",
       "      <td>18-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1999</td>\n",
       "      <td>170.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.135798</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>146</th>\n",
       "      <td>Belgrano</td>\n",
       "      <td>DEF</td>\n",
       "      <td>Erik Godoy</td>\n",
       "      <td>29</td>\n",
       "      <td>8/16/1993</td>\n",
       "      <td>16-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1993</td>\n",
       "      <td>185.0</td>\n",
       "      <td>Buenos Aires</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.220356</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>202</th>\n",
       "      <td>Platense</td>\n",
       "      <td>MED</td>\n",
       "      <td>Franco Diaz</td>\n",
       "      <td>22</td>\n",
       "      <td>8/28/2000</td>\n",
       "      <td>28-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>2000</td>\n",
       "      <td>180.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.192957</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>219</th>\n",
       "      <td>Belgrano</td>\n",
       "      <td>MED</td>\n",
       "      <td>Gabriel Compagnucci</td>\n",
       "      <td>31</td>\n",
       "      <td>8/29/1991</td>\n",
       "      <td>29-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1991</td>\n",
       "      <td>178.0</td>\n",
       "      <td>Monte Buey</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.181784</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>246</th>\n",
       "      <td>Def y Justicia</td>\n",
       "      <td>MED</td>\n",
       "      <td>Gonzalo Castellani</td>\n",
       "      <td>35</td>\n",
       "      <td>8/10/1987</td>\n",
       "      <td>10-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1987</td>\n",
       "      <td>183.0</td>\n",
       "      <td>Buenos Aires</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.209486</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>248</th>\n",
       "      <td>Central Cba (SdE)</td>\n",
       "      <td>DEF</td>\n",
       "      <td>Gonzalo Goñi</td>\n",
       "      <td>24</td>\n",
       "      <td>8/16/1998</td>\n",
       "      <td>16-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1998</td>\n",
       "      <td>187.0</td>\n",
       "      <td>Pedro Luro</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.231109</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>265</th>\n",
       "      <td>Newells</td>\n",
       "      <td>DEF</td>\n",
       "      <td>Guillermo Ortíz</td>\n",
       "      <td>30</td>\n",
       "      <td>8/9/1992</td>\n",
       "      <td>09-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1992</td>\n",
       "      <td>183.0</td>\n",
       "      <td>Rosario</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.209486</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>279</th>\n",
       "      <td>Atl Tucuman</td>\n",
       "      <td>MED</td>\n",
       "      <td>Ignacio Maestro Puch</td>\n",
       "      <td>19</td>\n",
       "      <td>8/13/2003</td>\n",
       "      <td>13-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>2003</td>\n",
       "      <td>180.0</td>\n",
       "      <td>San Miguel de Tucuman</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.192957</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>282</th>\n",
       "      <td>Platense</td>\n",
       "      <td>MED</td>\n",
       "      <td>Ignacio Schor</td>\n",
       "      <td>22</td>\n",
       "      <td>8/4/2000</td>\n",
       "      <td>04-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>2000</td>\n",
       "      <td>183.0</td>\n",
       "      <td>Buenos Aires</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.209486</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>343</th>\n",
       "      <td>Rosario Central</td>\n",
       "      <td>DEF</td>\n",
       "      <td>Juan Cruz Komar</td>\n",
       "      <td>26</td>\n",
       "      <td>8/13/1996</td>\n",
       "      <td>13-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1996</td>\n",
       "      <td>190.0</td>\n",
       "      <td>Rosario</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.247024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>368</th>\n",
       "      <td>Talleres (C)</td>\n",
       "      <td>DEF</td>\n",
       "      <td>Julio Buffarini</td>\n",
       "      <td>34</td>\n",
       "      <td>8/18/1988</td>\n",
       "      <td>18-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1988</td>\n",
       "      <td>172.0</td>\n",
       "      <td>Gral. Cabrera</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.147494</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>410</th>\n",
       "      <td>Huracan</td>\n",
       "      <td>ARQ</td>\n",
       "      <td>Lucas Chaves</td>\n",
       "      <td>27</td>\n",
       "      <td>8/9/1995</td>\n",
       "      <td>09-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1995</td>\n",
       "      <td>179.0</td>\n",
       "      <td>Martín Coronado</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.187386</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>416</th>\n",
       "      <td>Velez</td>\n",
       "      <td>DEL</td>\n",
       "      <td>Lucas Janson</td>\n",
       "      <td>28</td>\n",
       "      <td>8/16/1994</td>\n",
       "      <td>16-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1994</td>\n",
       "      <td>171.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.141664</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>424</th>\n",
       "      <td>Argentinos</td>\n",
       "      <td>DEF</td>\n",
       "      <td>Lucas Villalba</td>\n",
       "      <td>28</td>\n",
       "      <td>8/19/1994</td>\n",
       "      <td>19-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1994</td>\n",
       "      <td>177.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.176150</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>442</th>\n",
       "      <td>Belgrano</td>\n",
       "      <td>ARQ</td>\n",
       "      <td>Manuel Vicentini</td>\n",
       "      <td>32</td>\n",
       "      <td>8/29/1990</td>\n",
       "      <td>29-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1990</td>\n",
       "      <td>187.0</td>\n",
       "      <td>Santa Fé</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.231109</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>459</th>\n",
       "      <td>Tigre</td>\n",
       "      <td>DEF</td>\n",
       "      <td>Martín Ortega</td>\n",
       "      <td>23</td>\n",
       "      <td>8/20/1999</td>\n",
       "      <td>20-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1999</td>\n",
       "      <td>183.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.209486</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>467</th>\n",
       "      <td>Talleres (C)</td>\n",
       "      <td>DEF</td>\n",
       "      <td>Matías Catalán</td>\n",
       "      <td>30</td>\n",
       "      <td>8/19/1992</td>\n",
       "      <td>19-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1992</td>\n",
       "      <td>172.0</td>\n",
       "      <td>Mar del Plata</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.147494</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>487</th>\n",
       "      <td>Central Cba (SdE)</td>\n",
       "      <td>MED</td>\n",
       "      <td>Mauro Pittón</td>\n",
       "      <td>28</td>\n",
       "      <td>8/8/1994</td>\n",
       "      <td>08-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1994</td>\n",
       "      <td>174.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.159055</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>502</th>\n",
       "      <td>Argentinos</td>\n",
       "      <td>DEF</td>\n",
       "      <td>Miguel Torrén</td>\n",
       "      <td>34</td>\n",
       "      <td>8/12/1988</td>\n",
       "      <td>12-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1988</td>\n",
       "      <td>179.0</td>\n",
       "      <td>Santa Fé</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.187386</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>504</th>\n",
       "      <td>Banfield</td>\n",
       "      <td>DEL</td>\n",
       "      <td>Milton Gimenez</td>\n",
       "      <td>26</td>\n",
       "      <td>8/12/1996</td>\n",
       "      <td>12-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1996</td>\n",
       "      <td>184.0</td>\n",
       "      <td>Grand Bourg</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.214936</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>545</th>\n",
       "      <td>Newells</td>\n",
       "      <td>MED</td>\n",
       "      <td>Pablo Pérez</td>\n",
       "      <td>37</td>\n",
       "      <td>8/10/1985</td>\n",
       "      <td>10-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1985</td>\n",
       "      <td>179.0</td>\n",
       "      <td>Rosario</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.187386</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>571</th>\n",
       "      <td>Argentinos</td>\n",
       "      <td>DEL</td>\n",
       "      <td>Rodrigo Cabral</td>\n",
       "      <td>22</td>\n",
       "      <td>8/8/2000</td>\n",
       "      <td>08-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>2000</td>\n",
       "      <td>170.0</td>\n",
       "      <td>Mercedes</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.135798</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>590</th>\n",
       "      <td>Instituto</td>\n",
       "      <td>DEL</td>\n",
       "      <td>Santiago Rodríguez</td>\n",
       "      <td>25</td>\n",
       "      <td>8/23/1997</td>\n",
       "      <td>23-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1997</td>\n",
       "      <td>171.0</td>\n",
       "      <td>San Luis</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.141664</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>598</th>\n",
       "      <td>Union</td>\n",
       "      <td>ARQ</td>\n",
       "      <td>Sebastián Moyano</td>\n",
       "      <td>32</td>\n",
       "      <td>8/26/1990</td>\n",
       "      <td>26-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1990</td>\n",
       "      <td>188.0</td>\n",
       "      <td>Mendoza</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.236442</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>629</th>\n",
       "      <td>Huracan</td>\n",
       "      <td>MED</td>\n",
       "      <td>Valentín Burgoa</td>\n",
       "      <td>22</td>\n",
       "      <td>8/16/2000</td>\n",
       "      <td>16-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>2000</td>\n",
       "      <td>175.0</td>\n",
       "      <td>Guaymallén</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.164786</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>635</th>\n",
       "      <td>Velez</td>\n",
       "      <td>DEL</td>\n",
       "      <td>Walter Bou</td>\n",
       "      <td>29</td>\n",
       "      <td>8/25/1993</td>\n",
       "      <td>25-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1993</td>\n",
       "      <td>176.0</td>\n",
       "      <td>Concordia</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.170484</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                Equipo Puesto               Jugador  Edad Nacimiento dia_mes  \\\n",
       "0                Tigre    MED         Aaron Molinas    22   8/2/2000  02-ago   \n",
       "67       Independiente    DEL       Braian Martínez    23  8/18/1999  18-ago   \n",
       "146           Belgrano    DEF            Erik Godoy    29  8/16/1993  16-ago   \n",
       "202           Platense    MED           Franco Diaz    22  8/28/2000  28-ago   \n",
       "219           Belgrano    MED   Gabriel Compagnucci    31  8/29/1991  29-ago   \n",
       "246     Def y Justicia    MED    Gonzalo Castellani    35  8/10/1987  10-ago   \n",
       "248  Central Cba (SdE)    DEF          Gonzalo Goñi    24  8/16/1998  16-ago   \n",
       "265            Newells    DEF       Guillermo Ortíz    30   8/9/1992  09-ago   \n",
       "279        Atl Tucuman    MED  Ignacio Maestro Puch    19  8/13/2003  13-ago   \n",
       "282           Platense    MED         Ignacio Schor    22   8/4/2000  04-ago   \n",
       "343    Rosario Central    DEF       Juan Cruz Komar    26  8/13/1996  13-ago   \n",
       "368       Talleres (C)    DEF       Julio Buffarini    34  8/18/1988  18-ago   \n",
       "410            Huracan    ARQ          Lucas Chaves    27   8/9/1995  09-ago   \n",
       "416              Velez    DEL          Lucas Janson    28  8/16/1994  16-ago   \n",
       "424         Argentinos    DEF        Lucas Villalba    28  8/19/1994  19-ago   \n",
       "442           Belgrano    ARQ      Manuel Vicentini    32  8/29/1990  29-ago   \n",
       "459              Tigre    DEF         Martín Ortega    23  8/20/1999  20-ago   \n",
       "467       Talleres (C)    DEF        Matías Catalán    30  8/19/1992  19-ago   \n",
       "487  Central Cba (SdE)    MED          Mauro Pittón    28   8/8/1994  08-ago   \n",
       "502         Argentinos    DEF         Miguel Torrén    34  8/12/1988  12-ago   \n",
       "504           Banfield    DEL        Milton Gimenez    26  8/12/1996  12-ago   \n",
       "545            Newells    MED           Pablo Pérez    37  8/10/1985  10-ago   \n",
       "571         Argentinos    DEL        Rodrigo Cabral    22   8/8/2000  08-ago   \n",
       "590          Instituto    DEL    Santiago Rodríguez    25  8/23/1997  23-ago   \n",
       "598              Union    ARQ      Sebastián Moyano    32  8/26/1990  26-ago   \n",
       "629            Huracan    MED       Valentín Burgoa    22  8/16/2000  16-ago   \n",
       "635              Velez    DEL            Walter Bou    29  8/25/1993  25-ago   \n",
       "\n",
       "     nro_mes   año  Altura_cm             Ciudad_nac   Pais_nac  Altura_log  \n",
       "0          8  2000      175.0                    NaN  Argentina    5.164786  \n",
       "67         8  1999      170.0                    NaN  Argentina    5.135798  \n",
       "146        8  1993      185.0           Buenos Aires  Argentina    5.220356  \n",
       "202        8  2000      180.0                    NaN  Argentina    5.192957  \n",
       "219        8  1991      178.0             Monte Buey  Argentina    5.181784  \n",
       "246        8  1987      183.0           Buenos Aires  Argentina    5.209486  \n",
       "248        8  1998      187.0             Pedro Luro  Argentina    5.231109  \n",
       "265        8  1992      183.0                Rosario  Argentina    5.209486  \n",
       "279        8  2003      180.0  San Miguel de Tucuman  Argentina    5.192957  \n",
       "282        8  2000      183.0           Buenos Aires  Argentina    5.209486  \n",
       "343        8  1996      190.0                Rosario  Argentina    5.247024  \n",
       "368        8  1988      172.0          Gral. Cabrera  Argentina    5.147494  \n",
       "410        8  1995      179.0        Martín Coronado  Argentina    5.187386  \n",
       "416        8  1994      171.0                    NaN  Argentina    5.141664  \n",
       "424        8  1994      177.0                    NaN  Argentina    5.176150  \n",
       "442        8  1990      187.0               Santa Fé  Argentina    5.231109  \n",
       "459        8  1999      183.0                    NaN  Argentina    5.209486  \n",
       "467        8  1992      172.0          Mar del Plata  Argentina    5.147494  \n",
       "487        8  1994      174.0                    NaN  Argentina    5.159055  \n",
       "502        8  1988      179.0               Santa Fé  Argentina    5.187386  \n",
       "504        8  1996      184.0            Grand Bourg  Argentina    5.214936  \n",
       "545        8  1985      179.0                Rosario  Argentina    5.187386  \n",
       "571        8  2000      170.0               Mercedes  Argentina    5.135798  \n",
       "590        8  1997      171.0               San Luis  Argentina    5.141664  \n",
       "598        8  1990      188.0                Mendoza  Argentina    5.236442  \n",
       "629        8  2000      175.0             Guaymallén  Argentina    5.164786  \n",
       "635        8  1993      176.0              Concordia  Argentina    5.170484  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Como hacemos un filtro un poco mas complicado?\n",
    "\n",
    "# Elijamos las personas que nacieron en Agosto, en Argentina y su altura es mayor que 150 cm\n",
    "\n",
    "df_filtered = df[(df['nro_mes'] == 8) & (df['Altura_cm'] > 150) & (df['Pais_nac'] == 'Argentina')]\n",
    "\n",
    "display(df_filtered)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "id": "sextO4P4y6i4"
   },
   "outputs": [
    {
     "data": {
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       "    .dataframe thead th {\n",
       "        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>Equipo</th>\n",
       "      <th>Puesto</th>\n",
       "      <th>Jugador</th>\n",
       "      <th>Edad</th>\n",
       "      <th>Nacimiento</th>\n",
       "      <th>dia_mes</th>\n",
       "      <th>nro_mes</th>\n",
       "      <th>año</th>\n",
       "      <th>Altura_cm</th>\n",
       "      <th>Ciudad_nac</th>\n",
       "      <th>Pais_nac</th>\n",
       "      <th>Altura_log</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Tigre</td>\n",
       "      <td>MED</td>\n",
       "      <td>Aaron Molinas</td>\n",
       "      <td>22</td>\n",
       "      <td>8/2/2000</td>\n",
       "      <td>Esto es una prueba</td>\n",
       "      <td>8</td>\n",
       "      <td>2000</td>\n",
       "      <td>175.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.164786</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>67</th>\n",
       "      <td>Independiente</td>\n",
       "      <td>DEL</td>\n",
       "      <td>Braian Martínez</td>\n",
       "      <td>23</td>\n",
       "      <td>8/18/1999</td>\n",
       "      <td>18-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1999</td>\n",
       "      <td>170.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.135798</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>146</th>\n",
       "      <td>Belgrano</td>\n",
       "      <td>DEF</td>\n",
       "      <td>Erik Godoy</td>\n",
       "      <td>29</td>\n",
       "      <td>8/16/1993</td>\n",
       "      <td>16-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1993</td>\n",
       "      <td>185.0</td>\n",
       "      <td>Buenos Aires</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.220356</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>202</th>\n",
       "      <td>Platense</td>\n",
       "      <td>MED</td>\n",
       "      <td>Franco Diaz</td>\n",
       "      <td>22</td>\n",
       "      <td>8/28/2000</td>\n",
       "      <td>28-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>2000</td>\n",
       "      <td>180.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.192957</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>219</th>\n",
       "      <td>Belgrano</td>\n",
       "      <td>MED</td>\n",
       "      <td>Gabriel Compagnucci</td>\n",
       "      <td>31</td>\n",
       "      <td>8/29/1991</td>\n",
       "      <td>29-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1991</td>\n",
       "      <td>178.0</td>\n",
       "      <td>Monte Buey</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.181784</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>246</th>\n",
       "      <td>Def y Justicia</td>\n",
       "      <td>MED</td>\n",
       "      <td>Gonzalo Castellani</td>\n",
       "      <td>35</td>\n",
       "      <td>8/10/1987</td>\n",
       "      <td>10-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1987</td>\n",
       "      <td>183.0</td>\n",
       "      <td>Buenos Aires</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.209486</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>248</th>\n",
       "      <td>Central Cba (SdE)</td>\n",
       "      <td>DEF</td>\n",
       "      <td>Gonzalo Goñi</td>\n",
       "      <td>24</td>\n",
       "      <td>8/16/1998</td>\n",
       "      <td>16-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1998</td>\n",
       "      <td>187.0</td>\n",
       "      <td>Pedro Luro</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.231109</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>265</th>\n",
       "      <td>Newells</td>\n",
       "      <td>DEF</td>\n",
       "      <td>Guillermo Ortíz</td>\n",
       "      <td>30</td>\n",
       "      <td>8/9/1992</td>\n",
       "      <td>09-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1992</td>\n",
       "      <td>183.0</td>\n",
       "      <td>Rosario</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.209486</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>279</th>\n",
       "      <td>Atl Tucuman</td>\n",
       "      <td>MED</td>\n",
       "      <td>Ignacio Maestro Puch</td>\n",
       "      <td>19</td>\n",
       "      <td>8/13/2003</td>\n",
       "      <td>13-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>2003</td>\n",
       "      <td>180.0</td>\n",
       "      <td>San Miguel de Tucuman</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.192957</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>282</th>\n",
       "      <td>Platense</td>\n",
       "      <td>MED</td>\n",
       "      <td>Ignacio Schor</td>\n",
       "      <td>22</td>\n",
       "      <td>8/4/2000</td>\n",
       "      <td>04-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>2000</td>\n",
       "      <td>183.0</td>\n",
       "      <td>Buenos Aires</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.209486</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>343</th>\n",
       "      <td>Rosario Central</td>\n",
       "      <td>DEF</td>\n",
       "      <td>Juan Cruz Komar</td>\n",
       "      <td>26</td>\n",
       "      <td>8/13/1996</td>\n",
       "      <td>13-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1996</td>\n",
       "      <td>190.0</td>\n",
       "      <td>Rosario</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.247024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>368</th>\n",
       "      <td>Talleres (C)</td>\n",
       "      <td>DEF</td>\n",
       "      <td>Julio Buffarini</td>\n",
       "      <td>34</td>\n",
       "      <td>8/18/1988</td>\n",
       "      <td>18-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1988</td>\n",
       "      <td>172.0</td>\n",
       "      <td>Gral. Cabrera</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.147494</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>410</th>\n",
       "      <td>Huracan</td>\n",
       "      <td>ARQ</td>\n",
       "      <td>Lucas Chaves</td>\n",
       "      <td>27</td>\n",
       "      <td>8/9/1995</td>\n",
       "      <td>09-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1995</td>\n",
       "      <td>179.0</td>\n",
       "      <td>Martín Coronado</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.187386</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>416</th>\n",
       "      <td>Velez</td>\n",
       "      <td>DEL</td>\n",
       "      <td>Lucas Janson</td>\n",
       "      <td>28</td>\n",
       "      <td>8/16/1994</td>\n",
       "      <td>16-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1994</td>\n",
       "      <td>171.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.141664</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>424</th>\n",
       "      <td>Argentinos</td>\n",
       "      <td>DEF</td>\n",
       "      <td>Lucas Villalba</td>\n",
       "      <td>28</td>\n",
       "      <td>8/19/1994</td>\n",
       "      <td>19-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1994</td>\n",
       "      <td>177.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.176150</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>442</th>\n",
       "      <td>Belgrano</td>\n",
       "      <td>ARQ</td>\n",
       "      <td>Manuel Vicentini</td>\n",
       "      <td>32</td>\n",
       "      <td>8/29/1990</td>\n",
       "      <td>29-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1990</td>\n",
       "      <td>187.0</td>\n",
       "      <td>Santa Fé</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.231109</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>459</th>\n",
       "      <td>Tigre</td>\n",
       "      <td>DEF</td>\n",
       "      <td>Martín Ortega</td>\n",
       "      <td>23</td>\n",
       "      <td>8/20/1999</td>\n",
       "      <td>20-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1999</td>\n",
       "      <td>183.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.209486</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>467</th>\n",
       "      <td>Talleres (C)</td>\n",
       "      <td>DEF</td>\n",
       "      <td>Matías Catalán</td>\n",
       "      <td>30</td>\n",
       "      <td>8/19/1992</td>\n",
       "      <td>19-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1992</td>\n",
       "      <td>172.0</td>\n",
       "      <td>Mar del Plata</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.147494</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>487</th>\n",
       "      <td>Central Cba (SdE)</td>\n",
       "      <td>MED</td>\n",
       "      <td>Mauro Pittón</td>\n",
       "      <td>28</td>\n",
       "      <td>8/8/1994</td>\n",
       "      <td>08-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1994</td>\n",
       "      <td>174.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.159055</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>502</th>\n",
       "      <td>Argentinos</td>\n",
       "      <td>DEF</td>\n",
       "      <td>Miguel Torrén</td>\n",
       "      <td>34</td>\n",
       "      <td>8/12/1988</td>\n",
       "      <td>12-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1988</td>\n",
       "      <td>179.0</td>\n",
       "      <td>Santa Fé</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.187386</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>504</th>\n",
       "      <td>Banfield</td>\n",
       "      <td>DEL</td>\n",
       "      <td>Milton Gimenez</td>\n",
       "      <td>26</td>\n",
       "      <td>8/12/1996</td>\n",
       "      <td>12-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1996</td>\n",
       "      <td>184.0</td>\n",
       "      <td>Grand Bourg</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.214936</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>545</th>\n",
       "      <td>Newells</td>\n",
       "      <td>MED</td>\n",
       "      <td>Pablo Pérez</td>\n",
       "      <td>37</td>\n",
       "      <td>8/10/1985</td>\n",
       "      <td>10-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1985</td>\n",
       "      <td>179.0</td>\n",
       "      <td>Rosario</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.187386</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>571</th>\n",
       "      <td>Argentinos</td>\n",
       "      <td>DEL</td>\n",
       "      <td>Rodrigo Cabral</td>\n",
       "      <td>22</td>\n",
       "      <td>8/8/2000</td>\n",
       "      <td>08-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>2000</td>\n",
       "      <td>170.0</td>\n",
       "      <td>Mercedes</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.135798</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>590</th>\n",
       "      <td>Instituto</td>\n",
       "      <td>DEL</td>\n",
       "      <td>Santiago Rodríguez</td>\n",
       "      <td>25</td>\n",
       "      <td>8/23/1997</td>\n",
       "      <td>23-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1997</td>\n",
       "      <td>171.0</td>\n",
       "      <td>San Luis</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.141664</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>598</th>\n",
       "      <td>Union</td>\n",
       "      <td>ARQ</td>\n",
       "      <td>Sebastián Moyano</td>\n",
       "      <td>32</td>\n",
       "      <td>8/26/1990</td>\n",
       "      <td>26-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1990</td>\n",
       "      <td>188.0</td>\n",
       "      <td>Mendoza</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.236442</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>629</th>\n",
       "      <td>Huracan</td>\n",
       "      <td>MED</td>\n",
       "      <td>Valentín Burgoa</td>\n",
       "      <td>22</td>\n",
       "      <td>8/16/2000</td>\n",
       "      <td>16-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>2000</td>\n",
       "      <td>175.0</td>\n",
       "      <td>Guaymallén</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.164786</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>635</th>\n",
       "      <td>Velez</td>\n",
       "      <td>DEL</td>\n",
       "      <td>Walter Bou</td>\n",
       "      <td>29</td>\n",
       "      <td>8/25/1993</td>\n",
       "      <td>25-ago</td>\n",
       "      <td>8</td>\n",
       "      <td>1993</td>\n",
       "      <td>176.0</td>\n",
       "      <td>Concordia</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>5.170484</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                Equipo Puesto               Jugador  Edad Nacimiento  \\\n",
       "0                Tigre    MED         Aaron Molinas    22   8/2/2000   \n",
       "67       Independiente    DEL       Braian Martínez    23  8/18/1999   \n",
       "146           Belgrano    DEF            Erik Godoy    29  8/16/1993   \n",
       "202           Platense    MED           Franco Diaz    22  8/28/2000   \n",
       "219           Belgrano    MED   Gabriel Compagnucci    31  8/29/1991   \n",
       "246     Def y Justicia    MED    Gonzalo Castellani    35  8/10/1987   \n",
       "248  Central Cba (SdE)    DEF          Gonzalo Goñi    24  8/16/1998   \n",
       "265            Newells    DEF       Guillermo Ortíz    30   8/9/1992   \n",
       "279        Atl Tucuman    MED  Ignacio Maestro Puch    19  8/13/2003   \n",
       "282           Platense    MED         Ignacio Schor    22   8/4/2000   \n",
       "343    Rosario Central    DEF       Juan Cruz Komar    26  8/13/1996   \n",
       "368       Talleres (C)    DEF       Julio Buffarini    34  8/18/1988   \n",
       "410            Huracan    ARQ          Lucas Chaves    27   8/9/1995   \n",
       "416              Velez    DEL          Lucas Janson    28  8/16/1994   \n",
       "424         Argentinos    DEF        Lucas Villalba    28  8/19/1994   \n",
       "442           Belgrano    ARQ      Manuel Vicentini    32  8/29/1990   \n",
       "459              Tigre    DEF         Martín Ortega    23  8/20/1999   \n",
       "467       Talleres (C)    DEF        Matías Catalán    30  8/19/1992   \n",
       "487  Central Cba (SdE)    MED          Mauro Pittón    28   8/8/1994   \n",
       "502         Argentinos    DEF         Miguel Torrén    34  8/12/1988   \n",
       "504           Banfield    DEL        Milton Gimenez    26  8/12/1996   \n",
       "545            Newells    MED           Pablo Pérez    37  8/10/1985   \n",
       "571         Argentinos    DEL        Rodrigo Cabral    22   8/8/2000   \n",
       "590          Instituto    DEL    Santiago Rodríguez    25  8/23/1997   \n",
       "598              Union    ARQ      Sebastián Moyano    32  8/26/1990   \n",
       "629            Huracan    MED       Valentín Burgoa    22  8/16/2000   \n",
       "635              Velez    DEL            Walter Bou    29  8/25/1993   \n",
       "\n",
       "                dia_mes  nro_mes   año  Altura_cm             Ciudad_nac  \\\n",
       "0    Esto es una prueba        8  2000      175.0                    NaN   \n",
       "67               18-ago        8  1999      170.0                    NaN   \n",
       "146              16-ago        8  1993      185.0           Buenos Aires   \n",
       "202              28-ago        8  2000      180.0                    NaN   \n",
       "219              29-ago        8  1991      178.0             Monte Buey   \n",
       "246              10-ago        8  1987      183.0           Buenos Aires   \n",
       "248              16-ago        8  1998      187.0             Pedro Luro   \n",
       "265              09-ago        8  1992      183.0                Rosario   \n",
       "279              13-ago        8  2003      180.0  San Miguel de Tucuman   \n",
       "282              04-ago        8  2000      183.0           Buenos Aires   \n",
       "343              13-ago        8  1996      190.0                Rosario   \n",
       "368              18-ago        8  1988      172.0          Gral. Cabrera   \n",
       "410              09-ago        8  1995      179.0        Martín Coronado   \n",
       "416              16-ago        8  1994      171.0                    NaN   \n",
       "424              19-ago        8  1994      177.0                    NaN   \n",
       "442              29-ago        8  1990      187.0               Santa Fé   \n",
       "459              20-ago        8  1999      183.0                    NaN   \n",
       "467              19-ago        8  1992      172.0          Mar del Plata   \n",
       "487              08-ago        8  1994      174.0                    NaN   \n",
       "502              12-ago        8  1988      179.0               Santa Fé   \n",
       "504              12-ago        8  1996      184.0            Grand Bourg   \n",
       "545              10-ago        8  1985      179.0                Rosario   \n",
       "571              08-ago        8  2000      170.0               Mercedes   \n",
       "590              23-ago        8  1997      171.0               San Luis   \n",
       "598              26-ago        8  1990      188.0                Mendoza   \n",
       "629              16-ago        8  2000      175.0             Guaymallén   \n",
       "635              25-ago        8  1993      176.0              Concordia   \n",
       "\n",
       "      Pais_nac  Altura_log  \n",
       "0    Argentina    5.164786  \n",
       "67   Argentina    5.135798  \n",
       "146  Argentina    5.220356  \n",
       "202  Argentina    5.192957  \n",
       "219  Argentina    5.181784  \n",
       "246  Argentina    5.209486  \n",
       "248  Argentina    5.231109  \n",
       "265  Argentina    5.209486  \n",
       "279  Argentina    5.192957  \n",
       "282  Argentina    5.209486  \n",
       "343  Argentina    5.247024  \n",
       "368  Argentina    5.147494  \n",
       "410  Argentina    5.187386  \n",
       "416  Argentina    5.141664  \n",
       "424  Argentina    5.176150  \n",
       "442  Argentina    5.231109  \n",
       "459  Argentina    5.209486  \n",
       "467  Argentina    5.147494  \n",
       "487  Argentina    5.159055  \n",
       "502  Argentina    5.187386  \n",
       "504  Argentina    5.214936  \n",
       "545  Argentina    5.187386  \n",
       "571  Argentina    5.135798  \n",
       "590  Argentina    5.141664  \n",
       "598  Argentina    5.236442  \n",
       "629  Argentina    5.164786  \n",
       "635  Argentina    5.170484  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Si quiero acceder a la fecha de nacimiento, del primer jugador de los que tenemos filtrados, como puedo hacer?\n",
    "\n",
    "# Primero el numero de fila, luego la columna a la que queremos entrar\n",
    "df_filtered.loc[0, 'dia_mes'] = 'Esto es una prueba'\n",
    "\n",
    "display(df_filtered)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Z9ebY5arG7r1"
   },
   "source": [
    "## Lambda functions\n",
    "En Python existe otra forma de declarar funciones además de la que vimos anteriormente, que es utilizando la palabra `lambda`. La función `promediar_dos_numeros` que vimos más temprano se escribiría de la siguiente forma\n",
    "\n",
    "```python\n",
    "promedio = lambda num1, num2: (num1 + num2) / 2\n",
    "\n",
    "```\n",
    "\n",
    "Los `lambda` son funciones \"anónimas\", y fueron introducidas a Python para código que sigue un estilo de programación llamado \"funcional\". Generalmente, la idea no es asignarla a una variable, sino usarla directamente dentro de otra función. Por ejemplo, la función `filter`:\n",
    "\n",
    "```python\n",
    "pares = list(filter(lambda x: x % 2 == 0, range(10)))\n",
    "```\n",
    "\n",
    "Lo introducimos por completitud, por si se la encuentran leyendo el código de otra persona, pero lo recomendado es definir funciones \"normales\" con `def`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "TCo6ZF4g962g"
   },
   "source": [
    "---\n",
    "\n",
    "# Histogramas\n",
    "\n",
    "Una cosita más que nos va a ser útil a la hora de dejar el Oriyin sin instalar es poder hacer histogramas. Con _pyplot_ eso lo podemos obtener de la función _hist_.\n",
    "\n",
    "Recordemos que en un histograma dividimos una serie de datos en rangos y contamos cuántos de nuestros datos caen en cada rango. A esos rangos se los llama _bins_.\n",
    "\n",
    "_hist_ toma como argumentos un array de números, en cuántos _bins_ queremos dividir a nuestro eje x y algunas otras opciones de color como constante de normalización y color de las barras.\n",
    "\n",
    "Hagamos un histograma simple de un set gaussiano. Para eso, creemos datos sintéticos usando ```random.normal``` de _NumPy_ . Esto de crear datos lo hacemos acá a modo de ejemplo, en la vida real uno importaria algun dataset de las formas que ya hemos visto."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "id": "KQj6HJf1962h"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n:\n",
      "[  6.   3.  18.  23.  56. 102. 127. 199. 236. 249. 261. 229. 191. 100.\n",
      "  85.  60.  36.  12.   5.   2.]\n",
      "\n",
      "bins:\n",
      "[ 52.42287041  57.21731723  62.01176405  66.80621087  71.6006577\n",
      "  76.39510452  81.18955134  85.98399817  90.77844499  95.57289181\n",
      " 100.36733863 105.16178546 109.95623228 114.7506791  119.54512593\n",
      " 124.33957275 129.13401957 133.92846639 138.72291322 143.51736004\n",
      " 148.31180686]\n"
     ]
    },
    {
     "data": {
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Lli3KyMhQRkaGHnroIY0dO1Y+n0+7du3SPffco3PPPVcjRoyQJPXr108jR47UbbfdpkWLFqmpqUlTp07VuHHjuIMHAABIOoVXUD7//HMNHDhQAwcOlCSVlJRo4MCBmjNnjhITE7V161Zdc801Ov/88zV58mRdeuml+vTTT5WSkhIeY8mSJerbt6+GDRum0aNH64orrtALL7zg3LMCAADtWptfQRk6dKhs2z7m8VWrVp1wjIyMDC1durStvxoAAHQQfBcPAAAwDoECAACMQ6AAAADjECgAAMA4BAoAADAOgQIAAIxDoAAAAOMQKAAAwDgECgAAMA6BAgAAjEOgAAAA4xAoAADAOAQKAAAwDoECAACMQ6AAAADjECgAAMA4BAoAADAOgQIAAIxDoAAAAOMQKAAAwDgECgAAMA6BAgAAjEOgAAAA4yTFegJAexIIBGRZlqNjVlZWqrm52dExAaC9I1CAkxQIBHTDjRNk1Tc6Om6o8aD8td+piUgBgDACBThJlmXJqm/UuUOmyZ2e49i4NRWbVbPqKbUQKAAQRqAAbeROz1F69z6OjResq3ZsLACIF1wkCwAAjEOgAAAA4xAoAADAOAQKAAAwDoECAACMQ6AAAADjECgAAMA4BAoAADAOgQIAAIxDoAAAAOMQKAAAwDgECgAAMA6BAgAAjEOgAAAA4xAoAADAOAQKAAAwDoECAACMQ6AAAADjECgAAMA4BAoAADAOgQIAAIxDoAAAAOMQKAAAwDgECgAAMA6BAgAAjEOgAAAA4xAoAADAOAQKAAAwDoECAACM0+ZAWbduna6++mplZ2fL5XLpnXfeiThu27bmzJmjrKwsdenSRYWFhdqxY0fEOXV1dSoqKpLb7VZaWpomT56sAwcOnNYTAQAA8SOprT/Q0NCgiy++WLfeequuv/76I47PmzdPzz33nF5++WX17t1bs2fP1ogRI7R9+3Z17txZklRUVKS9e/dq9erVampq0i233KIpU6Zo6dKlp/+M0OEFAgFZluX4uJWVlWpubnZ8XADAkdocKKNGjdKoUaOOesy2bT377LO6//77de2110qSXnnlFWVmZuqdd97RuHHj9PXXX2vlypXavHmzBg0aJEmaP3++Ro8erSeffFLZ2dmn8XTQ0QUCAd1w4wRZ9Y2Ojx1qPCh/7XdqIlIAIOraHCjHU1FRIb/fr8LCwvA+j8ej/Px8lZaWaty4cSotLVVaWlo4TiSpsLBQCQkJ2rhxo375y18eMW4oFFIoFAo/DgaDTk4bccSyLFn1jTp3yDS503McHbumYrNqVj2lFgIFZ1hz0yFVVlY6Pq7H45HX63V8XMAJjgaK3++XJGVmZkbsz8zMDB/z+/1H/AORlJSkjIyM8Dk/NnfuXD300ENOThVxzp2eo/TufRwdM1hX7eh4wMk42FCn6uoqTS+ZreTkZEfH9qR21pvLXiVSYCRHAyVaZs2apZKSkvDjYDCo3NzcGM4IAM6MplCD5OqkvMFT1d2X59i4we93a+em+bIsi0CBkRwNFJ/PJ0mqra1VVlZWeH9tba0uueSS8DmBQCDi55qbm1VXVxf++R9LSUlRSkqKk1MFgHYlNa2H468KAiZz9HNQevfuLZ/PpzVr1oT3BYNBbdy4UQUFBZKkgoIC7d+/X2VlZeFzPvroI7W2tio/P9/J6QAAgHaqza+gHDhwQDt37gw/rqio0JYtW5SRkaGePXvqzjvv1B/+8Aedd9554duMs7Ozdd1110mS+vXrp5EjR+q2227TokWL1NTUpKlTp2rcuHHcwQMAACSdQqB8/vnn+sUvfhF+fPjakEmTJmnx4sW655571NDQoClTpmj//v264oortHLlyvBnoEjSkiVLNHXqVA0bNkwJCQkaO3asnnvuOQeeDgAAiAdtDpShQ4fKtu1jHne5XHr44Yf18MMPH/OcjIwMPpQNAAAcE9/FAwAAjEOgAAAA4xAoAADAOAQKAAAwDoECAACMQ6AAAADjECgAAMA4BAoAADAOgQIAAIxDoAAAAOMQKAAAwDgECgAAMA6BAgAAjNPmbzMGAMSH5qZDqqysjMrYHo9HXq83KmOjYyBQAKADOthQp+rqKk0vma3k5GTHx/ekdtaby14lUnDKCBQA6ICaQg2Sq5PyBk9Vd1+eo2MHv9+tnZvmy7IsAgWnjEABgA4sNa2H0rv3ifU0gCNwkSwAADAOgQIAAIxDoAAAAOMQKAAAwDgECgAAMA6BAgAAjEOgAAAA4xAoAADAOAQKAAAwDoECAACMQ6AAAADjECgAAMA4BAoAADAOgQIAAIxDoAAAAOMQKAAAwDgECgAAMA6BAgAAjEOgAAAA4xAoAADAOAQKAAAwDoECAACMQ6AAAADjECgAAMA4BAoAADAOgQIAAIxDoAAAAOMQKAAAwDgECgAAME5SrCcAAIg/zU2HVFlZ6fi4Ho9HXq/X8XFhHgIFAOCogw11qq6u0vSS2UpOTnZ0bE9qZ7257FUipQMgUAAAjmoKNUiuTsobPFXdfXmOjRv8frd2bpovy7IIlA6AQAEAREVqWg+ld+8T62mgneIiWQAAYBwCBQAAGIe3eBAzgUBAlmU5OmZlZaWam5sdHRMAcOYRKIiJQCCgG26cIKu+0dFxQ40H5a/9Tk1ECgC0awQKYsKyLFn1jTp3yDS503McG7emYrNqVj2lFgIFANo1AgUx5U7PcfQq/2BdtWNjAQBih4tkAQCAcRwPlAcffFAulyti69u3b/h4Y2OjiouL1a1bN5199tkaO3asamtrnZ4GAABox6LyCsoFF1ygvXv3hrf169eHj911111avny53njjDa1du1Y1NTW6/vrrozENAADQTkXlGpSkpCT5fL4j9luWpRdffFFLly7VVVddJUl66aWX1K9fP23YsEGXXXZZNKYDAADamai8grJjxw5lZ2erT58+KioqUlVVlSSprKxMTU1NKiwsDJ/bt29f9ezZU6WlpcccLxQKKRgMRmwAACB+OR4o+fn5Wrx4sVauXKmFCxeqoqJCP//5z1VfXy+/36/k5GSlpaVF/ExmZqb8fv8xx5w7d648Hk94y83NdXraAADAII6/xTNq1Kjwny+66CLl5+erV69eWrZsmbp06XJKY86aNUslJSXhx8FgkEgBACCORf0247S0NJ1//vnauXOnfD6fDh06pP3790ecU1tbe9RrVg5LSUmR2+2O2AAAQPyKeqAcOHBAu3btUlZWli699FJ16tRJa9asCR8vLy9XVVWVCgoKoj0VAADQTjj+Fs/vfvc7XX311erVq5dqamr0wAMPKDExUePHj5fH49HkyZNVUlKijIwMud1uTZs2TQUFBdzBAwAAwhwPlN27d2v8+PHat2+funfvriuuuEIbNmxQ9+7dJUnPPPOMEhISNHbsWIVCIY0YMULPP/+809MAAADtmOOB8re//e24xzt37qwFCxZowYIFTv9qAAAQJ/guHgAAYBwCBQAAGIdAAQAAxiFQAACAcQgUAABgHAIFAAAYh0ABAADGIVAAAIBxCBQAAGAcAgUAABiHQAEAAMZx/Lt4AACIluamQ6qsrIzK2B6PR16vNypjo+0IFABAu3CwoU7V1VWaXjJbycnJjo/vSe2sN5e9SqQYgkABALQLTaEGydVJeYOnqrsvz9Gxg9/v1s5N82VZFoFiCAIFANCupKb1UHr3PrGeBqKMi2QBAIBxCBQAAGAcAgUAABiHQAEAAMYhUAAAgHEIFAAAYBwCBQAAGIdAAQAAxiFQAACAcQgUAABgHAIFAAAYh0ABAADGIVAAAIBx+DZjHFcgEJBlWY6PW1lZqebmZsfHBQDEBwIFxxQIBHTDjRNk1Tc6Pnao8aD8td+piUgBABwFgYJjsixLVn2jzh0yTe70HEfHrqnYrJpVT6mFQAEAHAWBghNyp+covXsfR8cM1lU7Oh4AIL5wkSwAADAOgQIAAIxDoAAAAONwDUqciMbtwNwKDACIFQIlDkTrdmBuBQYAxAqBEgeidTswtwIDAGKFQIkjTt8OzK3AAIBY4SJZAABgHAIFAAAYh0ABAADGIVAAAIBxuEgWAABJzU2HVFlZ6fi4Ho9HXq/X8XHjHYECAOjwDjbUqbq6StNLZis5OdnRsT2pnfXmsleJlDYiUAAAHV5TqEFydVLe4Knq7stzbNzg97u1c9N8WZZFoLQRgQIAwP9LTevh6OdJ4dRxkSwAADAOgQIAAIxDoAAAAOMQKAAAwDhcJHsUgUBAlmU5Pi73wgMAcHIIlB8JBAK64cYJsuobHR+be+EBADg5BMqPWJYlq75R5w6ZJnd6jmPjci88AHRM0fqEWim+X5knUI7BnZ7DvfAAgNMSzU+oleL7lXkC5QyKVkVXVlaqubnZ8XEBAKcnWp9QK8X/K/MxDZQFCxboiSeekN/v18UXX6z58+dryJAhsZxS1ESzokONB+Wv/U5NRAoAGIlPqG27mAXK66+/rpKSEi1atEj5+fl69tlnNWLECJWXl8dlCUazomsqNqtm1VNqIVAAoEOJ5+tbYhYoTz/9tG677TbdcsstkqRFixbpH//4h/7617/q3nvvjdW0oi4aFR2sq3Z0PACA+eL9+paYBMqhQ4dUVlamWbNmhfclJCSosLBQpaWlR5wfCoUUCoXCjw9/RkkwGHR8bgcOHFBLS7P21X6jQ6EGx8bd/12lbLtVdYGdSnC1ODZuNMdmzmdm7PY452iOzZzPzNjM+cyMHc05/3vPNtlKVLefjJYnI8vRsQ8e+E6BXcu1Z88ede7c2bFxD/9327btE59sx8CePXtsSfZnn30WsX/GjBn2kCFDjjj/gQcesCWxsbGxsbGxxcFWXV19wlZoF3fxzJo1SyUlJeHHra2tqqurU7du3eRyuWI4s+gKBoPKzc1VdXW13G53rKfTYbDuscG6xwbrHhsddd1t21Z9fb2ys7NPeG5MAuWcc85RYmKiamtrI/bX1tbK5/MdcX5KSopSUlIi9qWlpUVzikZxu90d6i+wKVj32GDdY4N1j42OuO4ej+ekzovJlwUmJyfr0ksv1Zo1a8L7WltbtWbNGhUUFMRiSgAAwCAxe4unpKREkyZN0qBBgzRkyBA9++yzamhoCN/VAwAAOq6YBcqvf/1r/fvf/9acOXPk9/t1ySWXaOXKlcrMzIzVlIyTkpKiBx544Ii3txBdrHtssO6xwbrHBut+Yi7bPpl7fQAAAM6cmFyDAgAAcDwECgAAMA6BAgAAjEOgAAAA4xAoBtizZ48mTJigbt26qUuXLhowYIA+//zz8HHbtjVnzhxlZWWpS5cuKiws1I4dO2I44/jQ0tKi2bNnq3fv3urSpYvy8vL0yCOPRHxHBGt/+tatW6err75a2dnZcrlceueddyKOn8wa19XVqaioSG63W2lpaZo8ebIOHDhwBp9F+3O8dW9qatLMmTM1YMAAnXXWWcrOztZNN92kmpqaiDFY97Y70d/3/3X77bfL5XLp2WefjdjPuv8HgRJj33//vS6//HJ16tRJ77//vrZv366nnnpK6enp4XPmzZun5557TosWLdLGjRt11llnacSIEWpsbIzhzNu/xx9/XAsXLtSf//xnff3113r88cc1b948zZ8/P3wOa3/6GhoadPHFF2vBggVHPX4ya1xUVKRt27Zp9erVWrFihdatW6cpU6acqafQLh1v3X/44Qd98cUXmj17tr744gu99dZbKi8v1zXXXBNxHuvedif6+37Y22+/rQ0bNhz1I99Z9/93+l/9h9Mxc+ZM+4orrjjm8dbWVtvn89lPPPFEeN/+/fvtlJQU+7XXXjsTU4xbY8aMsW+99daIfddff71dVFRk2zZrHw2S7Lfffjv8+GTWePv27bYke/PmzeFz3n//fdvlctl79uw5Y3Nvz3687kezadMmW5L97bff2rbNujvhWOu+e/duu0ePHvZXX31l9+rVy37mmWfCx1j3/+IVlBj7+9//rkGDBulXv/qVvF6vBg4cqL/85S/h4xUVFfL7/SosLAzv83g8ys/PV2lpaSymHDd+9rOfac2aNfrmm28kSf/85z+1fv16jRo1ShJrfyaczBqXlpYqLS1NgwYNCp9TWFiohIQEbdy48YzPOV5ZliWXyxX+njPWPTpaW1s1ceJEzZgxQxdccMERx1n3/2oX32Ycz/71r39p4cKFKikp0X333afNmzdr+vTpSk5O1qRJk+T3+yXpiE/YzczMDB/Dqbn33nsVDAbVt29fJSYmqqWlRY8++qiKiookibU/A05mjf1+v7xeb8TxpKQkZWRk8L+DQxobGzVz5kyNHz8+/MV1rHt0PP7440pKStL06dOPepx1/y8CJcZaW1s1aNAgPfbYY5KkgQMH6quvvtKiRYs0adKkGM8uvi1btkxLlizR0qVLdcEFF2jLli268847lZ2dzdqjw2hqatKNN94o27a1cOHCWE8nrpWVlelPf/qTvvjiC7lcrlhPx3i8xRNjWVlZ6t+/f8S+fv36qaqqSpLk8/kkSbW1tRHn1NbWho/h1MyYMUP33nuvxo0bpwEDBmjixIm66667NHfuXEms/ZlwMmvs8/kUCAQijjc3N6uuro7/HU7T4Tj59ttvtXr16vCrJxLrHg2ffvqpAoGAevbsqaSkJCUlJenbb7/V3XffrZ/85CeSWPf/RaDE2OWXX67y8vKIfd9884169eolSerdu7d8Pp/WrFkTPh4MBrVx40YVFBSc0bnGmx9++EEJCZH/CCQmJqq1tVUSa38mnMwaFxQUaP/+/SorKwuf89FHH6m1tVX5+flnfM7x4nCc7NixQx9++KG6desWcZx1d97EiRO1detWbdmyJbxlZ2drxowZWrVqlSTWPUKsr9Lt6DZt2mQnJSXZjz76qL1jxw57yZIldteuXe1XX301fM4f//hHOy0tzX733XftrVu32tdee63du3dv++DBgzGcefs3adIku0ePHvaKFSvsiooK+6233rLPOecc+5577gmfw9qfvvr6evvLL7+0v/zyS1uS/fTTT9tffvll+G6Rk1njkSNH2gMHDrQ3btxor1+/3j7vvPPs8ePHx+optQvHW/dDhw7Z11xzjZ2Tk2Nv2bLF3rt3b3gLhULhMVj3tjvR3/cf+/FdPLbNuh9GoBhg+fLl9oUXXminpKTYffv2tV944YWI462trfbs2bPtzMxMOyUlxR42bJhdXl4eo9nGj2AwaP/2t7+1e/bsaXfu3Nnu06eP/fvf/z7iX9Cs/en7+OOPbUlHbJMmTbJt++TWeN++ffb48ePts88+23a73fYtt9xi19fXx+DZtB/HW/eKioqjHpNkf/zxx+ExWPe2O9Hf9x87WqCw7v/hsu3/+dhMAAAAA3ANCgAAMA6BAgAAjEOgAAAA4xAoAADAOAQKAAAwDoECAACMQ6AAAADjECgAAMA4BAoAADAOgQIAAIxDoAAAAOMQKAAAwDj/B4nY0AjzCtofAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Distribución gaussiana centrada en 100, con 15 de desviación estándar\n",
    "data = np.random.normal(100, 15, 2000)\n",
    "\n",
    "n, bins, patches = plt.hist(data, bins=20, edgecolor='black', facecolor='royalblue', alpha=0.75)\n",
    "# n la variable n se encuentran los datos del histograma\n",
    "# bins es un vector con los bordes de los rangos de datos\n",
    "# patches no nos interesa en general\n",
    "\n",
    "# OBS1: Si no saben qué cantidad de bines elegir, pueden dejarle la\n",
    "# eleccion a matplotlib, usando: bins='auto'\n",
    "\n",
    "# OBS2: Si quieren forzar bines específicos, pueden pasarle un array o lista\n",
    "# con los comienzos de cada bin. Ej:\n",
    "#\n",
    "#    Esto da bines de ancho 0.1:\n",
    "#    bins = [1, 1.1, 1.2, 1.3, 1.4, 1.5]\n",
    "#\n",
    "#    Indistintamente pueden usar cosas que ya vimos para generar ararys:\n",
    "#    bins = np.arange(1, 1.6, 0.1)\n",
    "\n",
    "print(f'n:\\n{n}\\n')\n",
    "print(f'bins:\\n{bins}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "id": "K7PJtxW0962h"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Si lo quisieramos normalizar el area hay que agregar una opcion mas que es density=True como para\n",
    "# que entienda que queremos ver la \"densidad de probabilidad\", forma cheta para decir: normalizar el area.\n",
    "\n",
    "n, bins, patches = plt.hist(data, bins=20, edgecolor='black', facecolor='royalblue', alpha=0.75, density=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "M3zTg3Fy962h"
   },
   "source": [
    "Y ya que estamos, para concientizar acerca de los peligros a la hora de la elección de *bins*, graficamos algunos histogramas superpuestos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "id": "q2C6GQa1962h"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n, bins, patches = plt.hist(data, bins=100, density=True, edgecolor='black', facecolor='royalblue', alpha=0.75)\n",
    "n, bins, patches = plt.hist(data, bins=20 , density=True, edgecolor='black', facecolor='purple'  , alpha=0.5)\n",
    "n, bins, patches = plt.hist(data, bins=2 , density=True, edgecolor='black', facecolor='indianred'  , alpha=0.3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "os9gI8VL962h"
   },
   "source": [
    "### Ejercicio 6\n",
    "\n",
    "La función `randn` que usamos nos brinda números aleatorios distribuidos de manera gaussiana (distribución normal).\n",
    "\n",
    "1. Con lo mostrado arriba, cree un histograma con una distribución normal (igual que como hicimos ya) y superpongale una curva teórica de una gausiana.\n",
    "\n",
    "    __AYUDA__: Busquen \"plot normal distribution python\", en particular busquen la librería `scipy`.\n",
    "\n",
    "2. Haga el mismo ejercicio de recién pero con números aleatorios distribuidos de manera _uniforme_\n",
    "\n",
    "3. Lo mismo pero con números con una distribución pareto, o la distribución que prefieran.\n",
    "\n",
    "_Info:_ https://docs.scipy.org/doc/numpy-1.14.0/reference/routines.random.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "jkcydFNN962i"
   },
   "source": [
    "---\n",
    "## Resolución de un sistema de ecuaciones diferenciales ordinarias (ODE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "CmCFnDGi962i"
   },
   "source": [
    "Vamos con un caso simple y conocido por la mayoría: el infaltable problema del péndulo. Arrancamos desde donde sabemos todos. (Donde sabemos todos? Si no saben de donde salió esto no se hagan problema, es solo algo físico, no lo podemos evitar)\n",
    "\n",
    "$$ \\frac{d^2\\theta}{dt^2} + \\omega^2 \\theta = 0$$\n",
    "\n",
    "con $\\omega^2 = \\frac{g}{l}$\n",
    "\n",
    "Para resolver numéricamente este problema, proponemos utilizar la función `odeint` de la biblioteca `scipy.integrate` (Otra opción podría ser la función `solve_ivp`, para problemas de valores iniciales), y esa función utiliza un método no taaaaan distinto al [método de Euler](https://es.wikipedia.org/wiki/M%C3%A9todo_de_Euler) para la solución de ODE's, (inserte conocimientos de Cálculo Numérico aquí, sí, dale, cursala antes de recibirte) por lo que, para un problema con derivadas de segundo orden debemos armar un sistema de ecuaciones de primer orden.\n",
    "\n",
    "Sea $\\phi = \\dot{\\theta} \\rightarrow \\dot{\\phi} = \\ddot{\\theta}$\n",
    "\n",
    "Nos queda entonces"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "upfUBhg0962i"
   },
   "source": [
    "$$\n",
    "\\begin{align}\n",
    "\\dot{\\theta} = \\phi \\\\\n",
    "\\dot{\\phi} = -\\omega^2 \\theta\n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "dDaJEPfA962i"
   },
   "source": [
    "o bien"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "5Zgo72_G962i"
   },
   "source": [
    "$$\n",
    "\\begin{equation}\n",
    "\\begin{pmatrix}\n",
    "\\dot{\\theta} \\\\\n",
    "\\dot{\\phi}\n",
    "\\end{pmatrix}\n",
    "=\n",
    " \\begin{pmatrix}\n",
    "  0 & 1  \\\\\n",
    "  -\\omega^2 & 0\n",
    " \\end{pmatrix}\n",
    "\\begin{pmatrix}\n",
    "\\theta \\\\\n",
    "\\phi\n",
    "\\end{pmatrix}\n",
    "\\end{equation}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "U2iDy-Ds962i"
   },
   "source": [
    "o también\n",
    "\n",
    "$$ \\dot{\\vec{X}} = A \\vec{X} $$\n",
    "\n",
    "Escencialmente, nuestro `odeint` va a intentar resolver ese sistema para distintos $t$ mientras le hayamos dado un valor inicial de donde comenzar. Nada demasiado extraño. Así que lo que la función va a necesitar es una función que tome como primer argumento $\\vec{X}$, segundo argumento $t$ (por ser la variable independiente) y luego los demás parametros que necesite (en este caso sean $g$ y $l$) y opere para obtener $\\dot{\\vec{X}}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "id": "J8BJtVwJ962i"
   },
   "outputs": [],
   "source": [
    "from scipy.integrate import odeint\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "id": "FZEzyKKf962i"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def ecdif(X, t, g, l):\n",
    "    theta, phi = X\n",
    "    omega2 = g/l\n",
    "    return [phi, -omega2 * theta]\n",
    "\n",
    "g = 9.8\n",
    "l = 2\n",
    "X0 = [np.pi/4, 0]  # Inicio a 45 grados con velocidad = 0\n",
    "t = np.linspace(0, 10, 101)\n",
    "solucion = odeint(ecdif, X0, t, args = (g,l))\n",
    "\n",
    "plt.plot(t,solucion[:,0], label = 'theta')\n",
    "plt.plot(t,solucion[:,1], label = 'phi')\n",
    "plt.title('Resolucion del pendulo')\n",
    "plt.xlabel('Tiempo')\n",
    "plt.ylabel('Valores')\n",
    "plt.grid(True)\n",
    "plt.legend(loc = 'best')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ertoUgzD962j"
   },
   "source": [
    "Si quieren ver otro ejemplo que esto, recomendamos el [resuelto](https://github.com/fifabsas/talleresfifabsas/blob/master/python/Extras/Fisica2/oscilador_forzado.py) que hizo un Ex-FIFA del oscilador con forzante sin aproximación y comparado con la solución analítica (sí, esa que sin aproximación no buscó nadie). También recomendamos, a cuento de esto, un pasito más en resolución de ODE's que es una [simulación](https://github.com/fifabsas/talleresfifabsas/blob/master/python/Extras/Fisica1/simulacion.ipynb) de uno de los ejercicios de F1, donde se arma una animación y una visualización más interactiva con la biblioteca `ipywidgets` de tantas otras posibles."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "X--JkuZr962j"
   },
   "source": [
    "### Ejercicio\n",
    "1. Resuelvan el oscilador armónico amortiguado con el parámetro $\\gamma$\n",
    "2. Vuelvan a todas esas guías que nadie terminó, busquen los ejercicios con asterisco, métanlos en Python y aprecien el poder del cálculo numérico."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "O-H8jqXf962j"
   },
   "source": [
    "---\n",
    "\n",
    "## Un poco de algebra lineal con *NumPy*\n",
    "\n",
    "NumPy trae muchas funciones para resolver problemas típicos de algebra lineal usando a los arrays como vectores. El que nos interesa en general es el de autovalores y autovectores y el sistema de ecuaciones lineales, pero empecemos con un ejemplo más fácil:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "id": "QNs8tiWP962j"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.7320508075688772\n",
      "1.7320508075688772\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# cargamos el módulo de algebra lineal\n",
    "from numpy import linalg\n",
    "v = np.array([1, 1, 1])\n",
    "w = np.array([2, 2, 2])\n",
    "z = np.array([1, 0, 1])\n",
    "\n",
    "norma =linalg.norm(v)  # la norma 2 / módulo del vector v\n",
    "print(norma)\n",
    "print(np.sqrt(v[0]**2 + v[1]**2 + v[2]**2))  # calculado a mano == sqrt(3)\n",
    "print(norma == np.sqrt(3))  # y numpy sabe que son lo mismo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "tlvBi-C1962j"
   },
   "source": [
    "Ahora si, usemos los vectores que creamos recién para crear una matriz y digamosle a _NumPy_ que calcule los autovectoresy autovalores de esa matriz:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "id": "gN8V4XrM962k"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Los autovalores: [ 3.41421356e+00 -1.23150120e-16  5.85786438e-01]\n",
      "\n",
      "Los autovectores: [[ 4.39732612e-01  7.07106781e-01 -3.03890631e-01]\n",
      " [ 8.79465224e-01 -1.09165123e-16 -6.07781262e-01]\n",
      " [ 1.82143212e-01 -7.07106781e-01  7.33656883e-01]]\n"
     ]
    }
   ],
   "source": [
    "matriz = np.array([v, w, z], dtype=np.float64)\n",
    "#eig devuelve una tupla de arrays con los autovalores en un array 1D y los autovec en un array 2D\n",
    "eigens = linalg.eig(matriz)\n",
    "\n",
    "autvals, autvecs = eigens\n",
    "\n",
    "print('Los autovalores:', autvals)\n",
    "print()\n",
    "print('Los autovectores:', autvecs)\n",
    "\n",
    "#se terminó el problema"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "8raIhKR9962k"
   },
   "source": [
    "Y para un sistema de ecuaciones del tipo $Ax = b$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "id": "rOJc7Tr9962k"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.67857143 0.07142857 0.03571429]\n"
     ]
    }
   ],
   "source": [
    "mat = np.array([[1, 2, 5], [2, 5, 8], [4, 0, 8]], dtype=np.float64)\n",
    "b = np.array([1, 2, 3])\n",
    "x = linalg.solve(mat, b)  # resuelve el sistema A*x = b\n",
    "print(x)\n",
    "\n",
    "# se terminó el problema"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "HpYidTEj962k"
   },
   "source": [
    "Por supuesto, también se puede hacer producto matriz con vector, y... oh si, se pueden calcular *inversas*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "id": "4p7XCsP8962k"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1. 2. 3.]\n",
      "[[-1.42857143  0.57142857  0.32142857]\n",
      " [-0.57142857  0.42857143 -0.07142857]\n",
      " [ 0.71428571 -0.28571429 -0.03571429]]\n"
     ]
    }
   ],
   "source": [
    "print(np.dot(mat,x))\n",
    "print(linalg.inv(mat))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "3G_G--wB962k"
   },
   "source": [
    "---\n",
    "\n",
    "### Ejercicio\n",
    "\n",
    "Parecen incrédulos. Fabriquen entonces la matriz\n",
    "$$\n",
    "\\begin{equation}\n",
    "A =\n",
    "\\begin{pmatrix}\n",
    "  0 & 1 \\\\\n",
    "  1 & 0  \n",
    "\\end{pmatrix}\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "cuyos autovalores son $\\lambda_1 = 1$ y $\\lambda_2 = -1 $, hallen sus autovalores y autovectores (a mano y con Python) y calculen $Ax$ con\n",
    "$$\n",
    "\\begin{equation}\n",
    "x =\n",
    "\\begin{pmatrix}\n",
    "1\\\\0\n",
    "\\end{pmatrix}\n",
    "\\end{equation}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "vAPW4KK4962l"
   },
   "source": [
    "---\n",
    "### Ejercicio\n",
    "\n",
    "Inventen una matriz de 5x5 (con el método que quieran y ¡que no sea la identidad!) y averigüen si es invertible. Si están prestando atención, saben que para resolver este problema les conviene ver la documentación de numpy.linalg.\n",
    "\n",
    "*Ayuda*: ¿Es necesario calcular la inversa? ¿Se acuerdan algo de álgebra lineal?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "CIyR9IN1962l"
   },
   "source": [
    "---\n",
    "\n",
    "# Cálculo simbólico"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "eYBAxJJm962l"
   },
   "source": [
    "Ahora no sólo nos vamos a emancipar del *Oriyin*, sino también del bendito *Wolfram Alpha* (Disclaimer: si bien la librería que se usa es muy buena, todavía no llega a tener el nivel de software como Mathematica, Maple, etc).\n",
    "Así es, Python nos va a permitir hacer cálculos simbólicos, como las integrales que nunca supimos calcular. Todo eso y más, en el paquete **SymPy**:\n",
    "\n",
    "Hemos dicho que en general no es una buena práctica, pero este es uno de los pocos casos para los cuales se justifica importar toda la librería."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "id": "kuI4A5Bi962l"
   },
   "outputs": [],
   "source": [
    "from sympy import *\n",
    "from sympy.abc import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "W1olTVDy962l"
   },
   "source": [
    "Les daremos ahora un breve tour por algunas de las funciones que nos ofrece *SymPy*. Así como *numpy* nos introdujo el array como tipo de variable, las expresiones algebraicas en *sympy* son del tipo *symbols*. Estas pueden representar números enteros, reales, funciones, etc.\n",
    "\n",
    "A diferencia de las librerías anteriores, en las cuales usualmente escribimos los comandos dentro de un archivo a ejectutar todo junto (*script*); a modo de demostración utilizaremos *SymPy* de forma *interactiva*. Esta es posiblemente la manera en la que usaron *Wolfram Alpha* o *Mathematica* (para quienes lo hayan hecho)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "CxxEcAOg962l"
   },
   "source": [
    "Vimos aquí que una cantidad de variables se definieron como *symbols* de distintos tipos.\n",
    "Veamos ahora algunas de las posibilidades que tenemos:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "id": "X5XqCDBK962l"
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x^{2} + 2 x y + y^{2}$"
      ],
      "text/plain": [
       "x**2 + 2*x*y + y**2"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expand( (x + y)**2 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "id": "_3BpC6FA962m"
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left(x - 1\\right) \\left(x + 1\\right) \\left(x^{2} - x + 1\\right) \\left(x^{2} + x + 1\\right)$"
      ],
      "text/plain": [
       "(x - 1)*(x + 1)*(x**2 - x + 1)*(x**2 + x + 1)"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "factor( x**6 - 1 )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "HY6jOTy1962m"
   },
   "source": [
    "Utilizando variables simbólicas de tipo integer, podemos hacer algunas sumatorias, por ejemplo, la famosa $$\\sum_{k=0}^{m}k$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "id": "NdPN4ENj962m"
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{m \\left(m + 1\\right)}{2}$"
      ],
      "text/plain": [
       "m*(m + 1)/2"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Sum(k, (k,0,m) ).doit().factor()  #el comando .doit() evalúa la suma"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "1Q3uw70F962m"
   },
   "source": [
    "O incluso algunas series, como $$ \\sum_{n=1}^{\\infty}\\frac{1}{n^2} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "id": "kwmMpZqV962m"
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\pi^{2}}{6}$"
      ],
      "text/plain": [
       "pi**2/6"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Sum(1/n**2, (n, 1, oo)).doit()  # el infinito se escribe como oo (dos o minúscula)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "D2cvgvFz962n"
   },
   "source": [
    "---\n",
    "Posiblemente si queremos algo de cálculo simbólico, sea para calcular derivadas e integrales que nos molesten. Veamos algunos ejemplos $\\dfrac{\\text{d}x^n}{\\text{d}x}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "id": "kxObFxZm962n"
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle n x^{n - 1}$"
      ],
      "text/plain": [
       "n*x**(n - 1)"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diff(x**n , x).simplify()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "K53CSEud962n"
   },
   "source": [
    "$$ \\frac{d}{dx}\\big(\\ \\sin(\\tan(8x))\\ \\big)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "id": "lVIREd40962n"
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left(8 \\tan^{2}{\\left(8 x \\right)} + 8\\right) \\cos{\\left(\\tan{\\left(8 x \\right)} \\right)}$"
      ],
      "text/plain": [
       "(8*tan(8*x)**2 + 8)*cos(tan(8*x))"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diff(sin(tan(8*x)), x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "id": "ndyUqaL5962o"
   },
   "outputs": [],
   "source": [
    "out = diff(sin(tan(8*x)), x).simplify()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "id": "45pXhy2R962p"
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{8 \\cos{\\left(\\tan{\\left(8 \\sqrt{y} \\right)} \\right)}}{\\cos^{2}{\\left(8 \\sqrt{y} \\right)}}$"
      ],
      "text/plain": [
       "8*cos(tan(8*sqrt(y)))/cos(8*sqrt(y))**2"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Podemos hacer sustituciones de simbolos por otros simbolos!!\n",
    "out.subs(x, sqrt(y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "id": "98T7KC_p962p"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8*cos(tan(64))/cos(64)**2 = -36.5316624851842\n"
     ]
    }
   ],
   "source": [
    "# Hasta podemos sustituir por valores numéricos y evaluar la funcion!!\n",
    "print(f\"{out.subs(x, 8)} = {out.subs(x, 8).evalf()}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "xf8_cHFd962p"
   },
   "source": [
    "Si alguno desconfia, puede verlo desde [WolframAlfa](https://www.wolframalpha.com/input/?i=%288+%2B+8*tan%2864%29**2%29*log%288%29*cos%28tan%2864%29%29+%2B+sin%28tan%2864%29%29%2F8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "TqZ6zIq-962p"
   },
   "source": [
    "---\n",
    "Otro ejemplo! Derivadas parciales: $\\dfrac{\\partial^2}{\\partial y \\partial x}\\left( x\\sin{y} \\right)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "id": "ljf-qGec962p"
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\cos{\\left(y \\right)}$"
      ],
      "text/plain": [
       "cos(y)"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diff(x*sin(y), x, y)  # qué pasa si en lugar de x,y ponemos y,y?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "aOF7nn_m962q"
   },
   "source": [
    "También se pueden hacer integrales indefinidas o definidas con dominio infinito/acotado, obviamente luego se podría reemplazar en la expresión final por algun valor numérico, si así se quisiera\n",
    "$$\\int \\dfrac{1}{1+x^2}\\text{d}x$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "id": "ySbc_4Sc962q"
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\operatorname{atan}{\\left(x \\right)}$"
      ],
      "text/plain": [
       "atan(x)"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "integrate(1/(1+x**2), x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "vIiA9_y9962q"
   },
   "source": [
    "$$\\int_{-\\infty}^{+\\infty} \\dfrac{\\sin(x)}{x}\\text{d}x$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "id": "RFle8Vrl962q"
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\pi$"
      ],
      "text/plain": [
       "pi"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "integrate( sin(x)/x, (x,-oo,oo) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "vJPWRHlX962q"
   },
   "source": [
    "---\n",
    "Algo importantisimo y fabuloso de Sympy (algo que sorprendentemente NO tiene Mathematica ni Matlab) es que a cualquier expresión, podemos envolverla en un `latex()` para que devuelva la misma expresión que renderizó, pero en el formato de $\\LaTeX$. Derecho para mandar al informe o trabajo sin tipearla."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "id": "Z9-WrUrC962q"
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left(8 \\tan^{2}{\\left(8 x \\right)} + 8\\right) \\log{\\left(x \\right)} \\cos{\\left(\\tan{\\left(8 x \\right)} \\right)} + \\frac{\\sin{\\left(\\tan{\\left(8 x \\right)} \\right)}}{x}$"
      ],
      "text/plain": [
       "(8*tan(8*x)**2 + 8)*log(x)*cos(tan(8*x)) + sin(tan(8*x))/x"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "out = diff(sin(tan(8*x))*log(x), x)\n",
    "out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "id": "2jbmPoSA962q"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Normal: (8*tan(8*x)**2 + 8)*log(x)*cos(tan(8*x)) + sin(tan(8*x))/x\n",
      "LaTeX: \\left(8 \\tan^{2}{\\left(8 x \\right)} + 8\\right) \\log{\\left(x \\right)} \\cos{\\left(\\tan{\\left(8 x \\right)} \\right)} + \\frac{\\sin{\\left(\\tan{\\left(8 x \\right)} \\right)}}{x}\n"
     ]
    }
   ],
   "source": [
    "print(f\"Normal: {out}\")\n",
    "print(f\"LaTeX: {latex(out)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "-RLymUU6962r"
   },
   "source": [
    "### Ejercicio"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "mgtwvL9L962r"
   },
   "source": [
    "Calculen la siguiente integral:  $$ \\int_{-\\infty}^{+\\infty} e^{-x^2} \\text{d}x $$ (opcional: verificar el resultado a mano!)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Q-Q3z26J962r"
   },
   "source": [
    "---\n",
    "# Integración numérica\n",
    "Siempre es útil tener a mano una rutina de integración numérica. Puede ser para el caso en el cual la integral analítica sea muy complicada o no estándar. También es fundamental para poder integrar datos obtenidos experimentalmente, sin asumir alguna función que los modele. Para ambos casos, el paquete relevante será `scipy.integrate`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "RC3J0M8Q962r"
   },
   "source": [
    "### A partir de una función predefinida\n",
    "En este caso, la función a importar es `quad`, porque usa un método de [cuadraturas](https://en.wikipedia.org/wiki/Numerical_integration#Quadrature_rules_based_on_interpolating_functions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "id": "SgaxatwB962s"
   },
   "outputs": [],
   "source": [
    "from scipy.integrate import quad"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "uNMiXoEJ962s"
   },
   "source": [
    "Definamos una función para ser integrada. A modo de ejemplo, calcularemos\n",
    "\n",
    "$$\\int_a^b \\dfrac{\\text{e}^{-x^2 / 2}}{\\sqrt{2\\pi}}\\text{d}x$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "id": "lYJ_LgaS962s"
   },
   "outputs": [],
   "source": [
    "def integrando(x): return np.exp(-x**2 / 2)/np.sqrt(2*np.pi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "XG-C7bdB962s"
   },
   "source": [
    "Ahora, llamamos a `quad` para integrar esta función entre $a=-1$ y $b=1$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "id": "ySfZTQwC962s"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.682689492137086 7.579375928402476e-15\n"
     ]
    }
   ],
   "source": [
    "a = -1\n",
    "b = 1\n",
    "integral, error = quad(integrando, a, b)\n",
    "print(integral, error)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "vjN2Vtlx962s"
   },
   "source": [
    "Podemos, con este método, incluso obtener la primitiva numéricamente. Por ejemplo\n",
    "\n",
    "$$F(x) = \\int_a^x \\dfrac{\\text{e}^{-t^2 / 2}}{\\sqrt{2\\pi}}\\text{d}t$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "id": "sAEC3Y9E962s"
   },
   "outputs": [],
   "source": [
    "# Definimos este dominio\n",
    "x = np.linspace(-5,5,100)\n",
    "\n",
    "# Ahora obtenemos la primitiva\n",
    "prim = np.zeros(x.size)\n",
    "\n",
    "for i in range(x.size):\n",
    "    prim[i], error = quad(integrando, a, x[i])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "fklWsmsQ962s"
   },
   "source": [
    "Veamos la gráfica para este dominio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {
    "id": "ms1tun5v962s"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7e3ddd747020>"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "\n",
    "plt.plot(x, integrando(x), 'b', label = 'integrando')\n",
    "plt.plot(x, prim, 'r', label = 'primitiva')\n",
    "plt.grid(True)\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "gJe4qqAN962t"
   },
   "source": [
    "---\n",
    "# Funciones especiales"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "66Niqv2P962t"
   },
   "source": [
    "Tal vez en algún momento de la vida nos encontremos con funciones más exóticas que el seno, coseno y exponenciales, funciones que las conocemos de nombre pero de graficarlas ni hablemos. Por suerte, la biblioteca *scipy* cuenta con abanico muy grande de estas funciones con nombre propio. En la documentación (bloque de ayuda del spyder) podemos encontrar la lista completa de funciones, buscando `scipy.special`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {
    "id": "LtHMxZRT962t"
   },
   "outputs": [],
   "source": [
    "import scipy.special as sp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "8l__cNHR962t"
   },
   "source": [
    "Empecemos graficando un ejemplo común en probabilidad, la *función error*:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {
    "id": "sLUtQHSu962t"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "x = np.linspace(-5,5,100)  # generamos el dominio\n",
    "y = sp.erf(x)  # llama a la función error de la librería\n",
    "\n",
    "plt.plot(x,y, label='función error')\n",
    "plt.grid(True)\n",
    "plt.legend(loc='best')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "w1MvwHrI962t"
   },
   "source": [
    "Dentro de las muchas funciones que nos ofrece la librería, otro ejemplo importante en la física son las *funciones de Bessel* $J_{\\nu}(x)$. Hay una función para cada valor del índice $\\nu$ (que llamamos orden). En la librería, se llaman con el comando `jv(i,x)`, donde la primer entrada corresponde al orden $\\nu$.\n",
    "Como demostración, veamos ahora algunos de sus gráficos:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "id": "QDA3Sseq962t"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Funciones de Bessel')"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "num = 500\n",
    "r = np.linspace(0,10,num)\n",
    "\n",
    "for i in range(5):\n",
    "    y_i = sp.jv(i,r)  # para cada i, grafica la función de orden i\n",
    "    plt.plot(r,y_i,label='orden {}'.format(i))\n",
    "    plt.legend(loc='best')\n",
    "plt.grid(True)\n",
    "plt.xlim(0, 10)\n",
    "plt.title('Funciones de Bessel')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "vD1okFNq962u"
   },
   "source": [
    "### Ejercicio"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "HYCHhzoQ962u"
   },
   "source": [
    "1. Busquen en la documentación la función *gamma*, y grafiquenla en el intervalo $\\left[-5,5\\right]$\n",
    "2. (Opcional) Googleen a ver qué es lo tan importante de esa función."
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "colab": {
   "provenance": []
  },
  "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": "3.12.3"
  },
  "vscode": {
   "interpreter": {
    "hash": "a42cd95ca9a57c6387dbbfdd995a278478871c13a93fa5b980ac93bb6d23c0e2"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}