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"text": ["<matplotlib.figure.Figure at 0x7f44dd292588>"], "metadata": {}}], "input": ["xgrid = np.linspace(-2, 3, 1000)\n", "pt.grid()\n", "pt.plot(xgrid, f(xgrid))"], "prompt_number": 4, "metadata": {}}, {"source": ["What's the true solution of $f(x)=0$?"], "cell_type": "markdown", "metadata": {}}, {"cell_type": "code", "language": "python", "collapsed": false, "outputs": [{"output_type": "stream", "text": ["0.69314718056\n", "0.0\n"], "stream": "stdout"}], "input": ["xtrue = np.log(2)\n", "print(xtrue)\n", "print(f(xtrue))"], "prompt_number": 5, "metadata": {}}, {"source": ["Now let's run Newton's method and keep track of the errors:"], "cell_type": "markdown", "metadata": {}}, {"cell_type": "code", "language": "python", "collapsed": false, "outputs": [], "input": ["errors = []\n", "x = 2\n", "xbefore = 3"], "prompt_number": 6, "metadata": {}}, {"source": ["At each iteration, print the current guess and the error."], "cell_type": "markdown", "metadata": {}}, {"cell_type": "code", "language": "python", "collapsed": false, "outputs": [{"output_type": "stream", "text": ["nan\n", "nan\n"], "stream": "stdout"}, {"output_type": "stream", "text": ["-c:1: RuntimeWarning: invalid value encountered in double_scalars\n"], "stream": "stderr"}], "input": ["slope = (f(x)-f(xbefore))/(x-xbefore)\n", "\n", "xbefore = x\n", "x = x - f(x)/slope\n", "print(x)\n", "errors.append(abs(x-xtrue))\n", "print(errors[-1])"], "prompt_number": 17, "metadata": {}}, {"cell_type": "code", "language": "python", "collapsed": false, "outputs": [{"output_type": "stream", "text": ["0.882400077493\n", "0.411823511031\n", "0.147482044876\n", "0.0276859623403\n", "0.00198268429064\n", "2.73106724006e-05\n", "2.70651508982e-08\n", "3.69593244898e-13\n", "1.11022302463e-16\n", "1.11022302463e-16\n", "nan\n"], "stream": "stdout"}], "input": ["for err in errors:\n", "    print(err)"], "prompt_number": 18, "metadata": {}}, {"source": ["* Do you have a hypothesis about the order of convergence?"], "cell_type": "markdown", "metadata": {}}, {"cell_type": "code", "language": "python", "collapsed": false, "outputs": [], "input": ["# Does not quite double the number of digits each round--unclear."], "prompt_number": 19, "metadata": {}}, {"source": ["------------\n", "Let's check:"], "cell_type": "markdown", "metadata": {}}, {"cell_type": "code", "language": "python", "collapsed": false, "outputs": [{"output_type": "stream", "text": ["0.504224909965\n", "0.619635842142\n", "0.612688428557\n", "0.657169643929\n", "0.644727394358\n", "0.655276572424\n", "0.648759771781\n", "14482.1405299\n", "7243300082.99\n", "nan\n"], "stream": "stdout"}], "input": ["for i in range(len(errors)-1):\n", "    print(errors[i+1]/errors[i]**1.618)"], "prompt_number": 22, "metadata": {}}]}], "metadata": {"name": "", "signature": "sha256:a60ba602d6e44082eeba5aa3f12c5d9cd459b115c27d37ab9ce827d98f4530b6"}}