Evan O'Connor added file figures/Data Viewer.ipynb  about 8 years ago

Commit id: 6a334b6a153b3cc080f70841ea2c1c3f2999f397

deletions | additions      

         

{  "metadata": {  "name": "",  "signature": "sha256:7caf39a5a2641bbada4205a8ea3385e888b158a93a400af63ef03ce6545b9fad"  },  "nbformat": 3,  "nbformat_minor": 0,  "worksheets": [  {  "cells": [  {  "cell_type": "code",  "collapsed": false,  "input": [  "from IPython.display import display\n",  "\n",  "from sympy.interactive import printing\n",  "printing.init_printing()\n",  "\n",  "from __future__ import division\n",  "import sympy as sym\n",  "from sympy import *\n",  "x, y, z = symbols(\"x y z\")\n",  "k, m, n = symbols(\"k m n\", integer=True)\n",  "f, g, h = map(Function, 'fgh')\n",  "\n",  "%matplotlib inline\n",  "import numpy as np\n",  "import matplotlib.pyplot as plt\n",  "plt.rc('figure', figsize=(10, 6))"  ],  "language": "python",  "metadata": {},  "outputs": [],  "prompt_number": 1  },  {  "cell_type": "code",  "collapsed": false,  "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": 2  },  {  "cell_type": "code",  "collapsed": false,  "input": [  "plot_taylor_approximations(sin, 0, [1, 4, 6], (0, 5*pi), (-2,2))"  ],  "language": "python",  "metadata": {},  "outputs": [  {  "metadata": {},  "output_type": "display_data",  "png": 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4hUYrY/Hp5LJyh5M7T0863+CXX8z6srFjafO4I0eAP/80/P0oHx809PTEe6Gh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\nOMJFbWTWrFl4/vnnMWPGDCQkJOCcxoW+h4cHZs6cienTp2PFihVtckw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