{"metadata": {"signature": "sha256:a1384defeacd8390e6acd6a96a6aeaf8fe1a1760bd67f7b57de4f1e386bbea07", "name": ""}, "nbformat_minor": 0, "worksheets": [{"metadata": {}, "cells": [{"metadata": {}, "cell_type": "markdown", "source": ["# Secant Method"]}, {"language": "python", "collapsed": false, "metadata": {}, "input": ["import numpy as np\n", "import matplotlib.pyplot as pt"], "cell_type": "code", "prompt_number": 1, "outputs": []}, {"metadata": {}, "cell_type": "markdown", "source": ["Here's a function: (Look here! No derivative.)"]}, {"language": "python", "collapsed": false, "metadata": {}, "input": ["def f(x):\n", " return x**3 - x +1\n", "\n", "xmesh = np.linspace(-2, 2, 100)\n", "pt.ylim([-3, 10])\n", "pt.grid()\n", "pt.plot(xmesh, f(xmesh))"], "cell_type": "code", "prompt_number": 3, "outputs": [{"metadata": {}, "output_type": "pyout", "text": ["[]"], "prompt_number": 3}, {"metadata": {}, "output_type": "display_data", "text": [""], "png": 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59xJQZma9Chsz67/HRO/WcM5NBT7qYJM0jGU2OSH5sax3ztVlvv8YeB3Yo9Vm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\n"}]}, {"language": "python", "collapsed": false, "metadata": {}, "input": ["guesses = [2, 1.5]"], "cell_type": "code", "prompt_number": 7, "outputs": []}, {"metadata": {}, "cell_type": "markdown", "source": ["Evaluate this cell many times in-place (using Ctrl-Enter)"]}, {"language": "python", "collapsed": false, "metadata": {}, "input": ["\n", "# grab last two guesses\n", "x = guesses[-1]\n", "xbefore = guesses[-2]\n", "\n", "slope = (f(x)-f(xbefore))/(x-xbefore)\n", "\n", "# plot approximate function\n", "pt.plot(xmesh, f(xmesh))\n", "pt.plot(xmesh, f(x) + slope*(xmesh-x))\n", "pt.plot(x, f(x), \"o\")\n", "pt.plot(xbefore, f(xbefore), \"o\")\n", "pt.ylim([-3, 10])\n", "pt.axhline(0, color=\"black\")\n", "\n", "# Compute approximate root\n", "xnew = x - f(x) / slope\n", "guesses.append(xnew)\n", "print(xnew)"], "cell_type": "code", "prompt_number": 30, "outputs": [{"output_type": "stream", "text": ["-1.3247179572447458\n"], "stream": "stdout"}, {"metadata": {}, "output_type": "display_data", "text": [""], "png": 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++gqaN4dFi6BGDU/CEhE5Lc3UT5K9ZHFp16WUK1mOX36B1q3h/feV0EUkNsVk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\nGPL/piHkgymROi8AAAAASUVORK5CYII=\n"}]}, {"language": "python", "collapsed": false, "metadata": {}, "input": [], "cell_type": "code", "outputs": []}]}], "nbformat": 3}