04 Reading and Graphing Data from a File.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Reading and Graphing Data from a File"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In [03 Graphing Data](03%20Graphing%20Data%20with%20Matplotlib.ipynb) we graphed a string of tab-delimted data (presumably copied from another file or program like Logger Pro, Tracker, or Excel perhaps).\n",
    "\n",
    "In this tutorial, we will read and graph data from a file using two different packages:\n",
    "\n",
    "1. [CSV](https://docs.python.org/3.6/library/csv.html)\n",
    "2. [pandas](http://pandas.pydata.org/)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Using the CSV package\n",
    "\n",
    "The `csv` package is used to read and write tabular data.\n",
    "\n",
    "First, import packages and use the matplotlib magic command to display graphs in the browser."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import csv #used for reading and parsing data from a text file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt #used for graphing\n",
    "import numpy as np #used for arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#show graphs inline\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Read Data\n",
    "\n",
    "The data in this example is from Young's Double Sit experiment. The data file is a tab-delimited list of photodiode voltages and x-positions of the photodiode."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of Data Points:  57\n"
     ]
    }
   ],
   "source": [
    "#open and read the file\n",
    "filename='04-files/double-slit-data.txt'\n",
    "datafile = csv.reader(open(filename, 'r'), delimiter='\\t')\n",
    "\n",
    "rows=[]\n",
    "voltages=[] #list of photodiode voltages\n",
    "xpositions=[] #list of x positions\n",
    "for row in datafile:\n",
    "    rows.append(row)\n",
    "    xpositions.append(float(row[0]))\n",
    "    voltages.append(float(row[1]))\n",
    "print(\"Number of Data Points: \",len(voltages))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Graph Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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NU0qn2IHbJCp0Av372zjE22/Hf26XDA/47t8BP4leJuRempmmSVeBoDSz0Dz+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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10aad3048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot graph\n",
    "fig1 = plt.figure()\n",
    "plt.title('Voltage vs. x-position')\n",
    "plt.xlabel('x (m)')\n",
    "plt.ylabel('V (volt)')\n",
    "plt.plot(xpositions,voltages,'b-')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using pandas to read data from a text file\n",
    "\n",
    "The `pandas` package is a Python tool for data structures and analysis. Its a common package for data science of various kinds. In this case, we will merely convert each column to an array and plot the arrays."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Read the data file and define a dataframe object (df for dataframe)\n",
    "df_all = pd.read_table('04-files/double-slit-data-with-header.txt')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x (m)</th>\n",
       "      <th>V (volts)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-2.6</td>\n",
       "      <td>0.08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-2.5</td>\n",
       "      <td>0.11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-2.4</td>\n",
       "      <td>0.18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-2.3</td>\n",
       "      <td>0.23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-2.2</td>\n",
       "      <td>0.29</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   x (m)  V (volts)\n",
       "0   -2.6       0.08\n",
       "1   -2.5       0.11\n",
       "2   -2.4       0.18\n",
       "3   -2.3       0.23\n",
       "4   -2.2       0.29"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#print first five rows of data with the header\n",
    "df_all.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(57, 2)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#print the dimensions of the data table\n",
    "df_all.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(57,)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#create an array of voltage data for all rows\n",
    "Varray = np.array(df_all['V (volts)'].tolist()) #create array\n",
    "Varray.shape #print the dimensions of the array\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(57,)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#create an array of position data for all rows\n",
    "xarray = np.array(df_all['x (m)'].tolist()) #create array\n",
    "xarray.shape #print the dimensions of the array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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NU0qn2IHbJCp0Av372zjE22/Hf26XDA/47t8BP4leJuRempmmSVeBoDSz0Dz+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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10cdf24e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot graph\n",
    "fig2 = plt.figure()\n",
    "plt.title('Voltage vs. x-position')\n",
    "plt.xlabel('x (m)')\n",
    "plt.ylabel('V (volt)')\n",
    "plt.plot(xarray,Varray,'b-')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}