NB

gistfile1.txt

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 "metadata": {
  "name": "",
  "signature": "sha256:37a992b67dcefc90d2e6c2b7333d2aed2e465f4053f120da258f9a664cbbb6e9"
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 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pylab\n",
      "import numpy\n",
      "import scipy.optimize\n",
      "import math\n",
      "import urllib.request"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 81
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def load_text_url(url):\n",
      "    response = urllib.request.urlopen(url)\n",
      "    return response.read().decode()\n",
      "\n",
      "def load_text_file(file_name):\n",
      "    with open(file_name, \"r\") as f:\n",
      "        return f.read()\n",
      "\n",
      "def read_pts_text(text):\n",
      "    return zip(*[[eval(c) for c in line.replace(\" \", \"\").split(\",\")] for line in text.split(\"\\n\")])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 87
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "text = load_text_url(\"https://gist.githubusercontent.com/agoose77/9d39d620974c443b35e7/raw/93429a21b5dce2dfaa6ab1d3a8be01045c4f61d2/Graph\")\n",
      "#text = load_text_file(\"D:/users/angus/documents/lab/boltzman/graph.csv\")\n",
      "\n",
      "x_pts, y_pts, y_err_pts = read_pts_text(text)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 89
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x_arr = numpy.array(x_pts)\n",
      "y_arr = numpy.array(y_pts)\n",
      "y_err_arr = numpy.array(y_err_pts)\n",
      "w_arr = 1 / numpy.sqrt(y_err_arr)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 90
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "f = lambda x, m, c: m * x + c\n",
      "(gradient, shift), covariance = scipy.optimize.curve_fit(f, x_arr, y_arr, sigma=w_arr)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 91
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pylab.clf()\n",
      "pylab.plot(x_arr, y_arr, 'rx')\n",
      "pylab.plot(x_arr, gradient * x_arr + shift, 'b-')\n",
      "pylab.errorbar(x_arr, y_arr, yerr=y_err_arr, linestyle=\"None\")\n",
      "pylab.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 92
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "T = 21.9 + 273.15\n",
      "e = 1.60217657e-19"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 93
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "kb = e / (T * gradient)\n",
      "print(kb)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1.66554221454e-23\n"
       ]
      }
     ],
     "prompt_number": 77
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "degrees_of_freedom = len(y_arr) - 2\n",
      "chi_sq = numpy.sum(w_arr * (f(x_arr, gradient, shift) - y_arr)**2)\n",
      "\n",
      "def err_gradient(x, y, w):\n",
      "    sum_w = numpy.sum(w)\n",
      "    return math.sqrt(sum_w / ((sum_w * numpy.sum(w * x ** 2)) - numpy.sum(w * x) ** 2))\n",
      "\n",
      "def err_intercept(x, y, w):\n",
      "    sum_w_x_sq = numpy.sum(w * x ** 2)\n",
      "    return math.sqrt(sum_w_x_sq / ((numpy.sum(w) * sum_w_x_sq) - numpy.sum(w * x) ** 2))\n",
      "\n",
      "def err_kb(e, m, T, err_m):\n",
      "    return (-e / (m**2 * T)) * err_m\n",
      "\n",
      "gradient_error = err_gradient(x_arr, y_arr, w_arr)\n",
      "intercept_error = err_intercept(x_arr, y_arr, w_arr)\n",
      "\n",
      "reduced_chi_sq = chi_sq / degrees_of_freedom\n",
      "\n",
      "print(reduced_chi_sq, gradient_error, intercept_error, err_kb(e, gradient, T, gradient_error))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "94.3572913537 0.7020988947163238 0.33784212278295217 -3.58669808881e-25\n"
       ]
      }
     ],
     "prompt_number": 78
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}