{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Importar Librerías Necesarias\n", "\n", "Para resolver EDOs mediante métodos numéricos usaremos el lenguaje de Python para su implementación, en específico utilizaremos Python3. Dos herramientas muy utilizadas y que nos servirán en este trabajo serán: la librería de arreglos de Numpy y la librería de gráficos Matplotlib.\n", "\n", "**Observación:** Las librerías antes mencionads no vienen por defecto dentro de Python, por lo que se es necesario instalarlas previamente para su uso. Se recomienda utilizar Anaconda, allí pueden usar el entorno de programación Spyder que contiene todas estas librerías y mucho más. También pueden usar los notebooks de google colab o Jupyter que también las poseen.\n", "(El comando !pip install nombre, permite instalar el paquete nombre, desde algún notebook, esto es necesario solo la primera vez en caso de nunca haber instalado ese paquete o que no venga, luego no es necesario utilizarlo nunca más)." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# Partimos importando ambas librerías como sigue\n", "import matplotlib.pyplot as plt \n", "import numpy as np \n", "\n", "# El comando \"as\" hace que cada vez que queramos llamar alguna función de estas\n", "# librerias solo tengamos que poner con antelación el nombre que se le haya\n", "# puesto, en estos casos, por convención, se suele utilizar \"np\" para Numpy y\n", "# y \"plt\" para matplotlib.pyplot" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Arreglos de Numpy\n", "\n", "Python posee sus propios arreglos, y en ellos podemos introducir strings, objetos, enteros, floats , etc. Además podemos modificar su tamaño y añadir elementos cuando queramos. Esto los hace que no sean arreglos formalmente hablando y les hace perder eficiencia, es por ello que utilizaremos los arreglos de Numpy, que resultan ser mucho más eficientes y además traen un montón de funciones útiles para su operatoria.\n", "\n", "Para crear arreglos en Numpy procesdemos como sigue:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Arreglo a = ['2' 'hola' 'tu' 'me' '1']\n", "Arreglo b = [ 1 2 3 4 5 6 7 8 9 10]\n" ] } ], "source": [ "# Creación de arreglos de numpy\n", "a = np.array([2,\"hola\",\"tu\",\"me\",1]) \n", "b = np.array([1,2,3,4,5,6,7,8,9,10])\n", "\n", "print(\"Arreglo a =\", a)\n", "print(\"Arreglo b =\", b)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "El primer elemento: 1\n", "El penúltimo elemento: 9\n", "El último elemento: 10\n", "Subconjunto del arreglo, por ejemplo, desde el elemento en la posición 3 al 7: [3 4 5 6 7]\n", "me, \n", "¿Es a[3] un entero?: False\n", "¿Es b[3] un entero?: False\n", "4, \n", "¿Es 2.0 un entero?: False\n", "¿Es 2 un entero?: True\n" ] } ], "source": [ "# Donde puedo pedir los elementos según su índice\n", "print(\"El primer elemento: \", b[0]) \n", "print(\"El penúltimo elemento: \", b[-2])\n", "print(\"El último elemento: \", b[-1])\n", "print(\"Subconjunto del arreglo, por ejemplo, desde el elemento en la posición 3 al 7: \", b[2:7]) \n", "\n", "# Observemos que el \"1\" que se coloco como un entero en el arreglo \"a\", al pedirlo\n", "# desde el arreglo, no arroja un entero. Esto es porque numpy necesita que los \n", "# elementos sean de un mismo tipo!\n", "print( a[3]+ \",\",type(a[3]))\n", "print(\"¿Es a[3] un entero?: \", type(a[3]) == int)\n", "print(\"¿Es b[3] un entero?: \", type(b[3]) == int)\n", "print( str(b[3])+ \",\",type(b[3]))\n", "c=2.0\n", "d=2\n", "print(\"¿Es\",c,\" un entero?: \", type(c) == int)\n", "print(\"¿Es\",d,\" un entero?: \", type(d) == int)" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Arreglo de unos: [1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n", "Arreglo de ceros: [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", "Arreglo de 10 enteros concecutivos: [0 1 2 3 4 5 6 7 8 9]\n", "Arreglo equiespaciado desde 0 a 10: [ 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.]\n", "['2' 'hola' 'tu' 'me' '1']\n", "me\n", "3\n" ] } ], "source": [ "# Funciones útiles de creación de arreglos \n", "b = np.ones(10) # arreglo de 10 unos \n", "c = np.zeros(10) # arreglo de 10 ceros \n", "d = np.arange(10) # arreglo de 10 enteros concecutivos desde el 0\n", "e = np.linspace(0,10,11) # arreglo equiespaciado, que parte en 0 y termina en 10 con 11 elementos\n", "f=[2.0,3.0,1.0]\n", "print(\"Arreglo de unos: \", b)\n", "print(\"Arreglo de ceros: \", c)\n", "print(\"Arreglo de 10 enteros concecutivos: \",d)\n", "print(\"Arreglo equiespaciado desde 0 a 10: \",e)\n", "print(a)\n", "print(a[int(f[1])]) #print(a[int(3.0)])\n", "print(round(2.9)) #round redondea" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Con la librería Numpy, no solo podemos definir arreglos, sino que también podemos definir y trabajar con matrices." ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Matriz cuadrada de ceros\n", "[[0. 0. 0.]\n", " [0. 0. 0.]\n", " [0. 0. 0.]]\n", "Matriz cuadrada de unos\n", "[[1. 1. 1.]\n", " [1. 1. 1.]\n", " [1. 1. 1.]]\n", "Matriz identidad 3x3\n", "[[1. 0. 0.]\n", " [0. 1. 0.]\n", " [0. 0. 1.]]\n", "Matriz identidad de 5x5\n", "[[1. 0. 0. 0. 0.]\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", "Matriz m2 modificada: \n", "[[1. 0. 0. 0. 0.]\n", " [0. 1. 0. 0. 0.]\n", " [0. 1. 2. 3. 4.]\n", " [0. 0. 0. 1. 0.]\n", " [0. 0. 0. 0. 1.]]\n" ] } ], "source": [ "m1 = np.zeros((3,3)) # Matriz de 3x3 de zeros\n", "print(\"Matriz cuadrada de ceros\")\n", "print(m1)\n", "\n", "m11 = np.ones((3,3)) # Matriz de 3x3 de unos\n", "print(\"Matriz cuadrada de unos\")\n", "print(m11)\n", "\n", "# Se puede acceder a estos números y modificarlos, transformémosla en la identidad\n", "m1[0][0] = 1 #m1[0,0]\n", "m1[1][1] = 1 #m1[1,1]\n", "m1[2][2] = 1 #m1[2,2]\n", "\n", "print(\"Matriz identidad 3x3\")\n", "print(m1)\n", "\n", "\n", "# O se puede obtener una matriz identidad de nxn más fácilmente con una función.\n", "m2 = np.identity(5)\n", "print(\"Matriz identidad de 5x5\")\n", "print(m2)\n", "\n", "# Se puede cambiar una fila completa\n", "a = np.arange(5)\n", "m2[2] = a\n", "\n", "print(\"Matriz m2 modificada: \")\n", "print(m2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Matplotlib\n", "\n", "Esta librería es aquella que nos permitirá hacer todo tipo de gráficos. \n", "\n", "Para ver su funcionalidad veamos el ejemplo de graficar la función $ f(x) = |\\sin(x)|$, entre $-2\\pi$ y $2\\pi$." ] }, { "cell_type": "code", "execution_count": 76, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Partimos definiendo 2 arreglos, uno que será el eje \"x\" y otro a rellenar con \n", "# los valores de la función en cada punto. Para que la gráfica sea posible, \n", "# ambos arreglos deben tener el mismo largo\n", "# Una función muy útil es linspace para el eje \"x\" gracias a su equiespaciado.\n", "x = np.linspace(-2*np.pi,2*np.pi,10)\n", "#print(x)\n", "y = np.zeros(10)\n", "\n", "# Creamos una función que haga la operatoria por nosotros usando Numpy\n", "def funcion(x):\n", " return np.absolute(np.sin(x))\n", "#print(funcion(3*np.pi/2))\n", " \n", "# recorremos el eje_y rellenando con los valores correspondientes\n", "for i in range(len(x)): #range(10)=[0,1,2,...,9]\n", " y[i] = funcion(x[i])\n", "\n", "#y=funcion(x), se podia en vez del for de arriba\n", "\n", "plt.plot(x,y,\"-g*\") # se crea la gráfica\n", "plt.show() # se muestra" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notamos que la función no se parece a lo que esperabamos, el problema aquí es que la gráfica se realiza uniendo todos los puntos con líneas rectas, por ende, mientras más puntos grafiquemos mejor será nuestro resultado en cuanto a \"suavidad\" de la gráfica.\n", "\n", "Le agregaremos más puntos, títulos, nombres a los ejes, color a la gráfica y le cambiaremos el tamaño." ] }, { "cell_type": "code", "execution_count": 84, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "n_p = 100 # Numeros de puntos (al considerar más puntos mas suave es la gráfica)\n", "x = np.linspace(-2*np.pi,2*np.pi,n_p)\n", "y = np.zeros(n_p)\n", "\n", "def funcion(x):\n", " return np.absolute(np.sin(x))\n", "\n", "for i in range(len(x)):\n", " y[i] = funcion(x[i])\n", "\n", "\n", "plt.figure(figsize=(10,10)) # cambio de tamaño\n", "plt.plot(x,y,\"r-o\") # gráfica y se añade color\n", "plt.xlabel(\"Valor de $x$\",size=20) # nombre al eje x\n", "plt.xticks(fontsize=20)\n", "plt.ylabel(\"Valor de $f(x)$\",size=20) # nombre al eje y\n", "plt.yticks(fontsize=20)\n", "plt.title(\"Valor absoluto del $|\\mathrm{sen}(x)|$\",size=20) # título\n", "plt.savefig(\"roberto.pdf\")\n", "plt.show() \n" ] }, { "cell_type": "code", "execution_count": 86, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "n_p = 1000 # Numeros de puntos (al considerar más puntos mas suave es la gráfica)\n", "t = np.linspace(0,8*np.pi,n_p)\n", "x = np.zeros(n_p)\n", "y = np.zeros(n_p)\n", "\n", "def funcion2(t):\n", " return np.exp(t)*np.cos(t) , np.exp(t)*np.sin(t) \n", "\n", "for i in range(len(t)):\n", " x[i],y[i] = funcion2(t[i])\n", "\n", "\n", "#x,y=funcion2(t)\n", "\n", "\n", "plt.figure(figsize=(8,8)) # cambio de tamaño\n", "plt.plot(x,y,\"g-*\") # gráfica y se añade color\n", "plt.xlabel(\"Valor de $x(t)$\",size=20) # nombre al eje x\n", "plt.xticks(fontsize=20)\n", "plt.ylabel(\"Valor de $y(t)$\",size=20) # nombre al eje y\n", "plt.yticks(fontsize=20)\n", "plt.title(\"Valor de Curva\",size=20) # título\n", "plt.show() \n" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.1" } }, "nbformat": 4, "nbformat_minor": 2 }