{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import numpy as np\n", "import numpy.linalg as la\n", "import matplotlib.pyplot as pt" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Truncation vs. Roundoff" ] }, { "cell_type": "code", "collapsed": false, "input": [ "c = 20*2*np.pi\n", "\n", "def f(x):\n", " return np.sin(c*x)\n", "\n", "def df(x):\n", " return c*np.cos(c*x)\n", "\n", "n = 2000\n", "x = np.linspace(0, 1, n, endpoint=False).astype(np.float32)\n", "\n", "plot(x, f(x))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 3, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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PPOnCVFCBv6+vD9ra2i7+vbW1Ffr6+qp+5tChQ1o/R6VxldalV8FQyQKwGKqz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\n7rjjDli8eDEsWLAAfvrTn7on6UDuuec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"text": [ "" ] } ], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "h_values = []\n", "err_values = []\n", "\n", "for n_exp in xrange(5, 24):\n", " n = 2**n_exp\n", " h = (1/n)\n", "\n", " x = np.linspace(0, 1, n, endpoint=False).astype(np.float32)\n", "\n", " fx = f(x)\n", " dfx = df(x)\n", "\n", " dfx_num = (np.roll(fx, -1) - np.roll(fx, 1)) / (2*h)\n", "\n", " err = np.max(np.abs((dfx - dfx_num))) / np.max(np.abs(fx))\n", "\n", " print h, err\n", "\n", " h_values.append(h)\n", " err_values.append(err)\n", "\n", "pt.rc(\"font\", size=16)\n", "pt.title(r\"Single precision FD error on $\\sin(20\\cdot 2\\pi)$\")\n", "pt.xlabel(r\"$h$\")\n", "pt.ylabel(r\"Rel. Error\")\n", "pt.loglog(h_values, err_values)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "0.03125 148.291\n", "0.015625 66.5355\n", "0.0078125 19.2357\n", "0.00390625 4.98669\n", "0.001953125 1.25798\n", "0.0009765625 0.318611\n", "0.00048828125 0.0862198\n", "0.000244140625 0.0271683\n", "0.0001220703125 0.0188675\n", "6.103515625e-05 0.0407867\n", "3.0517578125e-05 0.0859985\n", "1.52587890625e-05 0.163803\n", "7.62939453125e-06 0.336319\n", "3.81469726562e-06" ] }, { "output_type": "stream", "stream": "stdout", "text": [ " 0.663834\n", "1.90734863281e-06 1.66391\n", "9.53674316406e-07" ] }, { "output_type": "stream", "stream": "stdout", "text": [ " 2.33687\n", "4.76837158203e-07" ] }, { "output_type": "stream", "stream": "stdout", "text": [ " 5.66476\n", "2.38418579102e-07" ] }, { "output_type": "stream", "stream": "stdout", "text": [ " 13.6656\n", "1.19209289551e-07" ] }, { "output_type": "stream", "stream": "stdout", "text": [ " 29.6663\n" ] }, { "metadata": {}, "output_type": "pyout", "prompt_number": 4, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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fA6amwPz5YkeiO6j5jhBCBPDHH8B33/GzNsjo67/K6KUihBANy88Hpk7lk9LL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\nXOxoNIsxPhE5OPDNd4SU1yA7OmgLdXQ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"text": [ "" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Noise resistance" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def f(x):\n", " return 5*x**3\n", "\n", "def df(x):\n", " return 15*x**2" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 5 }, { "cell_type": "code", "collapsed": false, "input": [ "mesh = np.linspace(-1, 1, 100)\n", "h = mesh[1] - mesh[0]\n", "\n", "fx = f(mesh)\n", "dfx = df(mesh)\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 8, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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NBoMYNGhQns9hUlKSFaLXn4iICFG5cmXx8ssvi65duwqDwSCuXr1aqGOL+9m0\nahLIlpGRUeQk0KJFC2EymXLt+/TTT0XJkiXFzZs3lQ5R927duiVKliwpQkJCcu3v1KmTaNasWYHH\nDxw4UNSsWVOt8HRr9uzZwsnJSURHR+fsi4mJESVKlBCzZs165rGRkZHCYDCIZcuW5ezLyMgQDRs2\nFD169FAtZj2z5H4KIZPAxIkT1QzRpmRlZeX8vmjRokInAUs+m5qsJyCK2AwRHx+PkydPon///rn2\nDxgwAOnp6di6dauS4dmEbdu2IT09Pc89ya6Ku3r1aoHnKOp/B3uwadMmtGvXDnXr1s3Z5+npCT8/\nP2zcuLHAY52dnfHqq6/m7HNyckK/fv1y/ns4GkvuZzZH/Bw+TXG7y1vy2bSJRWWioqIA5B2H4Onp\nCXd3d5w7d06LsDQVFRUFFxeXPH2Fvb29AQBnz54t8Bx//PEHnnvuOTg7O6Nhw4aYMWOG3bexREVF\n5Tuexdvbu8B7FhUVhbp168LV1TXPsWlpaQ7Z3dmS+5nt22+/haurK0qVKoVOnTph//79Sodp9yz5\nbCq+noAasief8/DwyPOah4eHQ05Ol5CQkO/9qFChQs7rz+Lr64tWrVrBx8cHKSkp2LBhA8aNG4dL\nly5h0aJFqsSsB4mJiU+9b4mJic881tJ7bo8suZ+ALLkGBASgWrVqiI2NxcyZM+Hv748dO3agQ4cO\naoRslyz5bBY7CezcuRNdunQp8O9MJhN2795d3MsUyF6KksW5n5a89w8//DDXv7t164bSpUtjzpw5\nGDt2rGKjEYmeZfny5Tm/+/n5oWfPnmjSpAkmTpyIvXv3ahiZ4yh2EijqvEKWyM5w+X2zuHv3bk62\ns2VFvZ8eHh64e/duntezM35x7km/fv0we/ZsHDt2zG6TgIeHR76fo4SEhALvmYeHR77d9Sy557bO\nkvuZn9KlS6N79+5YunSpEuE5DEs+m8VOAkWdV8gSPj4+AIAzZ86gTZs2OftjY2ORlJSUUw9uy4p6\nP318fJCamoro6OhcD+zselh7uCdq8PHxwZkzZ/LsP3v2bIH3zMfHB2FhYUhJSclV93r27FmULFkS\n9erVUzxevbPkfj4L5xMrGks+mzbRMFyrVi00b94cq1atyrV/5cqVKFmyJF566SWNItPOSy+9BGdn\n53zvSdOmTVG7du0in3PVqlUwGAxo3bq1UmHqTo8ePXDo0CHExMTk7IuNjcXBgwfRo0ePAo9NT0/H\njz/+mLOWQNKoAAACPElEQVQvIyMD69atQ9euXeHs7Kxa3Hplyf3Mz/3797F582a7/gyqwaLPZrE6\nsxbT0aNHRWhoqFi3bp0wGAyib9++IjQ0VISGhuYaHOLv7y/q1auX69gtW7YIo9EohgwZIiIiInIG\ni40ZM8aab0FXxo4dK1xdXcWsWbNERESEGDp0qDAajeLXX3/N9Xd/vZ+xsbGiQ4cOYuHChWLHjh1i\n06ZN4s033xRGo1EMGzbM2m/DqvIb3NSsWbM8g5tiY2OFk5OT+PTTT3Md369fP+Hh4SEWL14sdu7c\nKYKCgoSbm5s4ceKEtd+KLlhyP2fOnCmGDh0q1q5dKyIiIsSyZctEkyZNhIuLi9i/f78Wb0cXsp+J\nQ4cOFQaDQXz77bciNDRU7NmzRwih/GfTqkkgODhYGAwGYTAYhNFozPX7kwMiTCaTqFOnTp7jN2zY\nIJo3by5cXFxE7dq1xWeffZZrcIWjyczMFFOmTBG1a9cWLi4uonnz5uKnn37K83d/vZ8JCQkiMDBQ\n1K5dW7i6ugp3d3fRsmVLMW/ePGuGr5m4uDgRFBQkypYtK8qUKSN69eqVZ0BOTExMvgMak5OTxahR\no0SVKlWEq6uraNu2bc7/nI6quPfzl19+EX5+fqJSpUrC2dlZVKxYUfTs2VMcPXrU2m9BV7Kfi399\nTnbs2FEIofxnU5UJ5IiIyDbYRJsAERGpg0mAiMiBMQkQETkwJgEiIgfGJEBE5MCYBIiIHBiTABGR\nA2MSICJyYEwCREQO7P8BZt5MlqPqB1wAAAAASUVORK5CYII=\n", "text": [ "" ] } ], "prompt_number": 8 }, { "cell_type": "code", "collapsed": false, "input": [ "fx_for_diff = fx\n", "fx_for_diff = fx + 0.05*np.random.randn(len(mesh))\n", "\n", "pt.plot(mesh, fx_for_diff)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 17, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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3Ltzd3TF79mx06dIFVatWhdFoLHZ9cMOGDQgICICbmxu8vb0xderU3BFJ9kgI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\n7BiTABGRHWMSICKyY0wCRER27P8AHrPOR7lNjlwAAAAASUVORK5CYII=\n", "text": [ "" ] } ], "prompt_number": 17 }, { "cell_type": "code", "collapsed": false, "input": [ "dfx_num = np.diff(fx_for_diff)/h\n", "pt.plot(mesh[:-1], dfx_num)\n", "pt.plot(mesh,dfx)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 18, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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37ysm9xSLhbc36+jz8qxvf0GBdWJBzsKxlJTor9BpTlRVKW9FrPV6LWKxZw8w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\n/0JsbCwCAgIwZMgQ/PLL/7d3fyFNvWEcwJ+ztb9ZNCqMoGY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