{ "metadata": { "name": "", "signature": "sha256:8562876461f022209dec8a7735a8c3f3db8a35856ffe2e1a0dd2100a157af1a2" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": false, "input": [ "name = '2015-07-27-least_squares'\n", "\n", "title = \"Simple least squares fit to study residuals\"" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "\n", "import os\n", "from datetime import datetime\n", "from IPython.core.display import HTML\n", "\n", "with open('creative_commons.txt', 'r') as f:\n", " html = f.read()\n", "\n", "\n", "hour = datetime.utcnow().strftime('%H:%M')\n", "comments=\"true\"\n", "\n", "\n", "date = '-'.join(name.split('-')[:3])\n", "slug = '-'.join(name.split('-')[3:])\n", "\n", "metadata = dict(title=title,\n", " date=date,\n", " hour=hour,\n", " comments=comments,\n", " slug=slug,\n", " name=name)\n", "\n", "markdown = \"\"\"Title: {title}\n", "date: {date} {hour}\n", "comments: {comments}\n", "slug: {slug}\n", "\n", "{{% notebook {name}.ipynb cells[2:] %}}\n", "\"\"\".format(**metadata)\n", "\n", "content = os.path.abspath(os.path.join(os.getcwd(),\n", " os.pardir,\n", " os.pardir, \n", " '{}.md'.format(name)))\n", "with open('{}'.format(content), 'w') as f:\n", " f.writelines(markdown)\n", " \n", "html = '''\n", "\n", "
This post was written as an IPython notebook.\n", " It is available for download\n", " or as a static html.
\n", "\n", "%s''' % (name, name, html)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "I got a question from a friend: how do I fit a function, using least-squares,\n", "to analyze the residuals. To answer that I cook this notebook up and made\n", "a post out of it ;-)\n", "\n", "For the example I create a fake tidal signal, that we want fit and remove,\n", "added some noise and an offset (mean current)." ] }, { "cell_type": "code", "collapsed": false, "input": [ "import numpy as np\n", "\n", "\n", "def fake_tide(t, M2amp, M2phase):\n", " \"\"\"\n", " Generate a minimally realistic-looking fake semidiurnal tide.\n", " \n", " t is time in hours\n", " phases are in radians\n", " \"\"\"\n", " out = M2amp * np.sin(2 * np.pi * t / 12.42 - M2phase)\n", " return out" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "N = 500\n", "res = 5\n", "noise = np.random.randn(N)\n", "\n", "t = np.arange(N)\n", "\n", "amp, phase = 2, 0\n", "\n", "u = fake_tide(t, amp, phase) + res + noise" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here is the signal we created." ] }, { "cell_type": "code", "collapsed": false, "input": [ "import matplotlib.pyplot as plt\n", "\n", "\n", "fig, ax = plt.subplots(figsize=(11, 2.75))\n", "ax.plot(t, u, 'darkgreen', label='Signal')\n", "leg = ax.legend()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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Jc4uRtouKFWhhDfpCCHgCDWVJaz2LVpuqkdwI2kLtCPuksZmzEf6i+0ITPfNo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\n6aWXcOSRRwIADjjgA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"text": [ "This post was written as an IPython notebook.\n", " It is available for download\n", " or as a static html.
\n", "\n", "