Alberto Pepe added file figures/curves/curves_notebook.ipynb  over 10 years ago

Commit id: 74d658dc9dea2f91bf6ba9266cffa532fdbbeeab

deletions | additions      

         

{  "metadata": {  "name": "curves_notebook"  },  "nbformat": 3,  "nbformat_minor": 0,  "worksheets": [  {  "cells": [  {  "cell_type": "markdown",  "metadata": {},  "source": "### Welcome to a Python notebook running within Authorea. \nThis is an example taken from http://nbviewer.ipython.org/ and it uses the SymPy package. \n\n#### How to get started\nIt's easy. ***Just click on the cell below and click Shift+Enter*** (Shift + Enter executes commands in IPython). This will load all the required packages to create the plot we are trying to recreate. "  },  {  "cell_type": "code",  "collapsed": false,  "input": "from IPython.display import display\n\nfrom sympy.interactive import printing\nprinting.init_printing()\n\nfrom __future__ import division\nimport sympy as sym\nfrom sympy import *\nx, y, z = symbols(\"x y z\")\nk, m, n = symbols(\"k m n\", integer=True)\nf, g, h = map(Function, 'fgh')\n\n%matplotlib inline\nimport numpy as np\nimport matplotlib.pyplot as plt\nplt.rc('figure', figsize=(10, 6))",  "language": "python",  "metadata": {},  "outputs": [],  "prompt_number": 5  },  {  "cell_type": "markdown",  "metadata": {},  "source": "Now, do the same for the cell below (which creates a function called _plot_taylor_approximations_). Click Shift+Enter and scroll down."  },  {  "cell_type": "code",  "collapsed": true,  "input": "def plot_taylor_approximations(func, x0=None, orders=(2, 4), xrange=(0,1), yrange=None, npts=200):\n \"\"\"Plot the Taylor series approximations to a function at various orders.\n\n Parameters\n ----------\n func : a sympy function\n x0 : float\n Origin of the Taylor series expansion. If not given, x0=xrange[0].\n orders : list\n List of integers with the orders of Taylor series to show. Default is (2, 4).\n xrange : 2-tuple or array.\n Either an (xmin, xmax) tuple indicating the x range for the plot (default is (0, 1)),\n or the actual array of values to use.\n yrange : 2-tuple\n (ymin, ymax) tuple indicating the y range for the plot. If not given,\n the full range of values will be automatically used. \n npts : int\n Number of points to sample the x range with. Default is 200.\n \"\"\"\n if not callable(func):\n raise ValueError('func must be callable')\n if isinstance(xrange, (list, tuple)):\n x = np.linspace(float(xrange[0]), float(xrange[1]), npts)\n else:\n x = xrange\n if x0 is None: x0 = x[0]\n xs = sym.Symbol('x')\n # Make a numpy-callable form of the original function for plotting\n fx = func(xs)\n f = sym.lambdify(xs, fx, modules=['numpy'])\n # We could use latex(fx) instead of str(), but matploblib gets confused\n # with some of the (valid) latex constructs sympy emits. So we play it safe.\n plt.plot(x, f(x), label=str(fx), lw=2)\n # Build the Taylor approximations, plotting as we go\n apps = {}\n for order in orders:\n app = fx.series(xs, x0, n=order).removeO()\n apps[order] = app\n # Must be careful here: if the approximation is a constant, we can't\n # blindly use lambdify as it won't do the right thing. In that case, \n # evaluate the number as a float and fill the y array with that value.\n if isinstance(app, sym.numbers.Number):\n y = np.zeros_like(x)\n y.fill(app.evalf())\n else:\n fa = sym.lambdify(xs, app, modules=['numpy'])\n y = fa(x)\n tex = sym.latex(app).replace('$', '')\n plt.plot(x, y, label=r'$n=%s:\\, %s$' % (order, tex) )\n \n # Plot refinements\n if yrange is not None:\n plt.ylim(*yrange)\n plt.grid()\n plt.legend(loc='best').get_frame().set_alpha(0.8)",  "language": "python",  "metadata": {},  "outputs": [],  "prompt_number": 6  },  {  "cell_type": "markdown",  "metadata": {},  "source": "Ok, we are almost done. If you hit Shift+Enter on the cell below, you will recreate the original plot on the Authorea page. Try it! ***Want to modify it? It's easy.*** Click on the cell below, modify the parameters of your choice, and then press Shift+Enter one more time. It should chnage accordingly. Enjoy! "  },  {  "cell_type": "code",  "collapsed": false,  "input": "plot_taylor_approximations(sin, 0, [2, 4, 6], (0, 5*pi), (-2,2))",  "language": "python",  "metadata": {},  "outputs": [  {  "metadata": {},  "output_type": "display_data",  "png": 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Y71pk2jR5Mg22QkJoWdEZlSlj2r08YQINvFyFbgZct9Ju4Y/Tf+C1kNcwf6HA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\nrKwMvXr1Qvfu3fHyyy+3quOKx4qy1nQMNATzop4mn8Ol0+kwdOhQmJi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"text": ""  }  ],  "prompt_number": 8  },  {  "cell_type": "code",  "collapsed": false,  "input": "",  "language": "python",  "metadata": {},  "outputs": []  }  ],  "metadata": {}  }  ]  }