{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": false, "input": [ "import numpy as np\n", "import matplotlib.pyplot as pt" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Task:** Approximate a function (here: by a line)" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def f(x):\n", " return - x**2 + 3*x\n", "\n", "def df(x):\n", " return -2*x + 3\n", "\n", "center = -1\n", "dist = 3\n", "grid = np.linspace(center-dist, center+dist, 100)\n", "\n", "fx = f(grid)\n", "pt.plot(grid, fx)\n", "pt.plot(grid, f(center) + df(center) * (grid-center))\n", "\n", "pt.xlim([grid[0], grid[-1]])\n", "pt.ylim([np.min(fx), np.max(fx)])" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 5, "text": [ "(-28.0, 2.2497704315886136)" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "* What's the error we see?\n", "* What if we make `dist` smaller?" ] } ], "metadata": {} } ] }