Why Pandas.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###**What is Pandas?**  Pandas is a python library for data analysis. It uses high-level data structures, and ways to manipulate them.  Pandas comes from data science, and works (almost) seamlessly with numpy and scipy."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Why use Pandas?**  Pandas makes it easy to manage complex data, munge data into submission, and perform scientific analysis. I've found it really fun to do science in Pandas!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Where to get started?** I personally love the book, \"Python for Data Analysis: Data Wrangling with Pandas, NumPy, and IPython\", by Wes McKinney, the inventor of Pandas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from IPython.display import Image, HTML\n",
    "import pandas  # Lots of people import pandas as pd for brevity\n",
    "import numpy as np\n",
    "import astropy.convolution\n",
    "from scipy.optimize import curve_fit\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"https://covers.oreillystatic.com/images/0636920023784/cat.gif\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Why should you use pandas?**  Pandas makes it easy to keep track of complex datasets.  You can visualize your data, manipulate, munge out bad data, filter, fit with models, bin and group, concatenate with other datasets, and export."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's dive in, and meet the basic part of pandas:  **pandas.DataFrame()**\n",
    "A DataFrame is like a dictionary-on-steroids.  Or like a spreadsheet with rows and columns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>wave</th>\n",
       "      <th>flam</th>\n",
       "      <th>noise</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>11436.9</td>\n",
       "      <td>-1.795000e-17</td>\n",
       "      <td>5.534000e-17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>11439.2</td>\n",
       "      <td>1.203000e-16</td>\n",
       "      <td>4.374000e-17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>11441.4</td>\n",
       "      <td>1.857000e-17</td>\n",
       "      <td>4.261000e-17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>11443.7</td>\n",
       "      <td>-1.751000e-16</td>\n",
       "      <td>3.584000e-17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>11446.0</td>\n",
       "      <td>-8.348000e-17</td>\n",
       "      <td>3.160000e-17</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      wave          flam         noise\n",
       "0  11436.9 -1.795000e-17  5.534000e-17\n",
       "1  11439.2  1.203000e-16  4.374000e-17\n",
       "2  11441.4  1.857000e-17  4.261000e-17\n",
       "3  11443.7 -1.751000e-16  3.584000e-17\n",
       "4  11446.0 -8.348000e-17  3.160000e-17"
      ]
     },
     "execution_count": 186,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Loading the Keck/Nirspec spectrum of a gravitationally lensed galaxy, \n",
    "# from Wuyts, Rigby, Gladders et al. 2014, The Astrophysical Journal,  781, 61\n",
    "df1 = pandas.read_table(\"Sample_data/rcs0327_knotU_N3_nirspeckeck.txt\", delim_whitespace=True, comment=\"#\")\n",
    "df1.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, df1 is a pandas dataframe that I read with read_table().  There are several read_ tools:  read_csv(), read_sql(), read_excel() ... you get the picture.  \n",
    "I wrote a tutorial on [reading astronomical data with pandas.](https://github.com/janerigby/astro-pandas-tutorials/blob/master/Get%20data%20into%20pandas.ipynb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's examine df1.  It looks like a spreadsheet, with rows and columns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Index([u'wave', u'flam', u'noise'], dtype='object')\n",
      "Index([u'wave', u'flam', u'noise'], dtype='object')\n"
     ]
    }
   ],
   "source": [
    "print df1.keys()\n",
    "print df1.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 1121 entries, 0 to 1120\n",
      "Data columns (total 3 columns):\n",
      "wave     1121 non-null float64\n",
      "flam     1107 non-null float64\n",
      "noise    1121 non-null float64\n",
      "dtypes: float64(3)\n",
      "memory usage: 26.3 KB\n"
     ]
    }
   ],
   "source": [
    "df1.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>wave</th>\n",
       "      <th>flam</th>\n",
       "      <th>noise</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1121.000000</td>\n",
       "      <td>1.107000e+03</td>\n",
       "      <td>1.121000e+03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>12819.974844</td>\n",
       "      <td>1.633409e-17</td>\n",
       "      <td>2.663281e-16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>830.235363</td>\n",
       "      <td>4.336269e-16</td>\n",
       "      <td>2.096674e-15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>11436.900000</td>\n",
       "      <td>-1.031000e-14</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>12096.000000</td>\n",
       "      <td>-5.886500e-19</td>\n",
       "      <td>3.083000e-18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>12793.100000</td>\n",
       "      <td>3.920000e-18</td>\n",
       "      <td>5.154000e-18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>13530.400000</td>\n",
       "      <td>1.009500e-17</td>\n",
       "      <td>1.115000e-17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>14310.200000</td>\n",
       "      <td>4.415000e-15</td>\n",
       "      <td>5.516000e-14</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               wave          flam         noise\n",
       "count   1121.000000  1.107000e+03  1.121000e+03\n",
       "mean   12819.974844  1.633409e-17  2.663281e-16\n",
       "std      830.235363  4.336269e-16  2.096674e-15\n",
       "min    11436.900000 -1.031000e-14  0.000000e+00\n",
       "25%    12096.000000 -5.886500e-19  3.083000e-18\n",
       "50%    12793.100000  3.920000e-18  5.154000e-18\n",
       "75%    13530.400000  1.009500e-17  1.115000e-17\n",
       "max    14310.200000  4.415000e-15  5.516000e-14"
      ]
     },
     "execution_count": 189,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 213,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1121, 5)"
      ]
     },
     "execution_count": 213,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>wave</th>\n",
       "      <th>flam</th>\n",
       "      <th>noise</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1118</th>\n",
       "      <td>14304.5</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1119</th>\n",
       "      <td>14307.4</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1120</th>\n",
       "      <td>14310.2</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         wave  flam  noise\n",
       "1118  14304.5   NaN    0.0\n",
       "1119  14307.4   NaN    0.0\n",
       "1120  14310.2   NaN    0.0"
      ]
     },
     "execution_count": 190,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1.tail(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>wave</th>\n",
       "      <th>flam</th>\n",
       "      <th>noise</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>11436.9</td>\n",
       "      <td>-1.795000e-17</td>\n",
       "      <td>5.534000e-17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>11439.2</td>\n",
       "      <td>1.203000e-16</td>\n",
       "      <td>4.374000e-17</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      wave          flam         noise\n",
       "0  11436.9 -1.795000e-17  5.534000e-17\n",
       "1  11439.2  1.203000e-16  4.374000e-17"
      ]
     },
     "execution_count": 191,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1.head(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "wave     1.431020e+04\n",
       "flam     4.415000e-15\n",
       "noise    5.516000e-14\n",
       "dtype: float64"
      ]
     },
     "execution_count": 192,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1060    4.415000e-15\n",
       "1069    2.689000e-15\n",
       "1037    1.624000e-15\n",
       "Name: flam, dtype: float64"
      ]
     },
     "execution_count": 193,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1['flam'].nlargest(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>wave</th>\n",
       "      <th>flam</th>\n",
       "      <th>noise</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    wave   flam  noise\n",
       "0  False  False  False\n",
       "1  False  False  False\n",
       "2  False  False  False"
      ]
     },
     "execution_count": 194,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1.isnull().head(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "wave      0\n",
       "flam     14\n",
       "noise     0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 195,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1.isnull().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>wave</th>\n",
       "      <th>flam</th>\n",
       "      <th>noise</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1107</th>\n",
       "      <td>14273.1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1108</th>\n",
       "      <td>14275.9</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1109</th>\n",
       "      <td>14278.8</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1110</th>\n",
       "      <td>14281.6</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1111</th>\n",
       "      <td>14284.5</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1112</th>\n",
       "      <td>14287.3</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1113</th>\n",
       "      <td>14290.2</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1114</th>\n",
       "      <td>14293.1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1115</th>\n",
       "      <td>14295.9</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1116</th>\n",
       "      <td>14298.8</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1117</th>\n",
       "      <td>14301.6</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1118</th>\n",
       "      <td>14304.5</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1119</th>\n",
       "      <td>14307.4</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1120</th>\n",
       "      <td>14310.2</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         wave  flam  noise\n",
       "1107  14273.1   NaN    0.0\n",
       "1108  14275.9   NaN    0.0\n",
       "1109  14278.8   NaN    0.0\n",
       "1110  14281.6   NaN    0.0\n",
       "1111  14284.5   NaN    0.0\n",
       "1112  14287.3   NaN    0.0\n",
       "1113  14290.2   NaN    0.0\n",
       "1114  14293.1   NaN    0.0\n",
       "1115  14295.9   NaN    0.0\n",
       "1116  14298.8   NaN    0.0\n",
       "1117  14301.6   NaN    0.0\n",
       "1118  14304.5   NaN    0.0\n",
       "1119  14307.4   NaN    0.0\n",
       "1120  14310.2   NaN    0.0"
      ]
     },
     "execution_count": 196,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# pandas.DataFrame.interpolate() can replace NaNs.  Use with care!\n",
    "# pandas.dropna() can drop the NaNs.  Use with care.\n",
    "df1.loc[df1['flam'].isnull()]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "wave     1.144370e+04\n",
       "flam    -1.751000e-16\n",
       "noise    3.584000e-17\n",
       "Name: 3, dtype: float64"
      ]
     },
     "execution_count": 197,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1.ix[3]  # Get one row, access by the index.  Clunky"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    False\n",
       "1    False\n",
       "2    False\n",
       "3    False\n",
       "4    False\n",
       "Name: wave, dtype: bool"
      ]
     },
     "execution_count": 198,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1['wave'].between(12793., 12799.).head()   # Boolean filter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>wave</th>\n",
       "      <th>flam</th>\n",
       "      <th>noise</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>560</th>\n",
       "      <td>12793.1</td>\n",
       "      <td>-3.087000e-18</td>\n",
       "      <td>7.239000e-18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>561</th>\n",
       "      <td>12795.7</td>\n",
       "      <td>5.561000e-19</td>\n",
       "      <td>8.453000e-18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>562</th>\n",
       "      <td>12798.3</td>\n",
       "      <td>9.950000e-18</td>\n",
       "      <td>1.047000e-17</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        wave          flam         noise\n",
       "560  12793.1 -3.087000e-18  7.239000e-18\n",
       "561  12795.7  5.561000e-19  8.453000e-18\n",
       "562  12798.3  9.950000e-18  1.047000e-17"
      ]
     },
     "execution_count": 199,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1.loc[df1['wave'].between(12793., 12799.)]   # Using that boolean filter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1236e12d0>"
      ]
     },
     "execution_count": 200,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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0/+Mf//BHHnnEu3XDjzwSP+2009w95u7n+TffpPuSJbO/91mIf2nOnh08t3Xr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\n/T/GBd3teenYsAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x123068650>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting shortcut:  pandas.DataFrame.plot() \n",
    "ax = df1.plot(x='wave', y='flam', color='k')\n",
    "df1.plot(x='wave', y='noise', color='yellow', ax=ax, label='uncert')\n",
    "plt.ylim(0,1E-15)\n",
    "plt.xlim(1.15E4, 1.38E4) # Can intermix regular matplotlib commands\n",
    "plt.xlabel(r\"observed wavelength ($\\AA$)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>wave</th>\n",
       "      <th>flam</th>\n",
       "      <th>noise</th>\n",
       "      <th>dispersion</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>11436.9</td>\n",
       "      <td>-1.795000e-17</td>\n",
       "      <td>5.534000e-17</td>\n",
       "      <td>2.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>11439.2</td>\n",
       "      <td>1.203000e-16</td>\n",
       "      <td>4.374000e-17</td>\n",
       "      <td>2.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>11441.4</td>\n",
       "      <td>1.857000e-17</td>\n",
       "      <td>4.261000e-17</td>\n",
       "      <td>2.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      wave          flam         noise  dispersion\n",
       "0  11436.9 -1.795000e-17  5.534000e-17         2.3\n",
       "1  11439.2  1.203000e-16  4.374000e-17         2.3\n",
       "2  11441.4  1.857000e-17  4.261000e-17         2.2"
      ]
     },
     "execution_count": 201,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#It's easy to add a new column to the dataframe\n",
    "df1['dispersion'] = df1['wave'].diff()\n",
    "df1['dispersion'].iloc[0] = df1['dispersion'][1] # Fill in the first value\n",
    "df1.head(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(11500.0, 13800.0)"
      ]
     },
     "execution_count": 202,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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c3QKuylFZzzpucU/2oOyMuMeLHNPz0BnSfX9CoVDW+NzTOYipM5b7GWecwZgx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\nQCVY/OgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12377d8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df1['smooth'] = df1['flam'].rolling(window=81, center=True).median()  # Rolling functions\n",
    "plt.plot(df1['wave'], df1['flam'], color='k')        # Plotting in regular matplotlib\n",
    "plt.plot(df1['wave'], df1['smooth'], color='green', lw=2)  # Smoothing example\n",
    "plt.ylim(0,0.1E-15)\n",
    "plt.xlim(1.15E4, 1.38E4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "560    12793.1\n",
      "561    12795.7\n",
      "562    12798.3\n",
      "Name: wave, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "# A pandas.Series() is a column (or a row) of a Pandas DataFrame\n",
    "example_series = df1.loc[df1['wave'].between(12793., 12799.)]['wave']\n",
    "print example_series"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12793.1 12793.1\n"
     ]
    }
   ],
   "source": [
    "# NumPy should work flawlessly on a Pandas Series or Dataframe\n",
    "print np.median(df1['wave']),   df1['wave'].median()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 12793.1  12795.7  12798.3]\n",
      "<type 'numpy.ndarray'>\n"
     ]
    }
   ],
   "source": [
    "# as_matrix() converts a pandas.Series or DataFrame to a numpy ndarray:\n",
    "print example_series.as_matrix()\n",
    "print type(example_series.as_matrix())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Some astropy and scipy functions will barf at a pandas.Series.  as_matrix() is the workaround\n",
    "boxcar = 21\n",
    "# This should barf:\n",
    "#smooth1 = astropy.convolution.convolve(df1['flam'], np.ones((boxcar,))/boxcar, boundary='extend', fill_value=np.nan)\n",
    "# But this should work:\n",
    "smooth1 = astropy.convolution.convolve(df1['flam'].as_matrix(), np.ones((boxcar,))/boxcar, boundary='extend', fill_value=np.nan)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 212,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1027, 5)"
      ]
     },
     "execution_count": 212,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1.dropna().shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1121 (1027, 5)\n",
      "(1e-15, 13523.907000000001, 30.0, 0.0)\n",
      "[  8.83609681e-16   1.35414973e+04   4.10266724e+00   6.23238583e-18]\n",
      "Flux was 9.08691976126e-15 erg/s/cm^2\n"
     ]
    },
    {
     "data": {
      "image/png": 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hFC0i0lkwcJ28mfpSh7AeoLZv386IESO4/vrrGT9+PK7rYtvZB9VSKhNtGWRW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\na9lG5+5FAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x124c98c10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Hack time:  \n",
    "# Fit the emission lines!  Measure the integrated flux of each emission line.\n",
    "# Bonus points: with uncertainties!\n",
    "# Hint #1: You may want to use scipy.optimize.curve_fit()\n",
    "# Hint #2: Unlike Pandas, scipy doesn't like NaN.  pandas.DataFrame.interpolate() or .dropna() can help\n",
    "rest_waves = np.array((4862.683, 4960.295, 5008.240))\n",
    "ax = df1.plot(x='wave', y='flam', color='k')\n",
    "df1.plot(x='wave', y='noise', color='yellow', ax=ax, label='uncert')\n",
    "plt.ylim(0,1E-15)\n",
    "plt.xlim(1.3E4, 1.36E4) \n",
    "plt.annotate(\"H\", xy=(1.315E4,0.2E-15), xycoords='data', fontsize=16)\n",
    "plt.annotate(\"O++\", xy=(1.34E4,0.4E-15), xycoords='data', fontsize=16)\n",
    "plt.annotate(\"O++\", xy=(1.355E4,0.8E-15), xycoords='data', fontsize=16)\n",
    "plt.xlabel(r\"observed wavelength ($\\AA$)\")\n",
    "##### REMOVE BELOW HERE FOR JANE'S SOLUTION\n",
    "# Below here is JRR's solution\n",
    "\n",
    "def onegaus(x, aa, bb, cc, cont): # Define a Gaussian with linear continuum\n",
    "    #y = np.zeros_like(x)\n",
    "    y = (aa * np.exp((x - bb)**2/(-2*cc**2))  + cont)\n",
    "    return y\n",
    "def fit_quick_gaussian(sp, guess_pars, colwave='wave', colf='flam', zz=0.) : # Gaussian fit to emission line.  Uses Pandas\n",
    "    # guess_pars are the initial guess at the Gaussian.\n",
    "    popt, pcov = curve_fit(onegaus, sp[colwave], sp[colf], p0=guess_pars)\n",
    "    fit = onegaus(sp[colwave], *popt)\n",
    "    return(popt, fit)\n",
    "def sum_of_gaussian(gauss_pars) :\n",
    "    (aa, bb, cc, cont) = gauss_pars\n",
    "    return( aa * cc * np.sqrt(2.0 * np.pi))\n",
    "\n",
    "print len(df1), df1.dropna().shape\n",
    "df2 = df1.dropna()\n",
    "guesspars = (1.E-15, 5007 *(1+1.701), 30., 0.0)\n",
    "(popt, fit) = fit_quick_gaussian(df2, guesspars, colwave='wave', colf='flam')\n",
    "plt.plot(df2['wave'], fit)\n",
    "print guesspars\n",
    "print popt\n",
    "print \"Flux was\", sum_of_gaussian(popt), \"erg/s/cm^2\"  # In counts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
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