Data Analysis/Usage of Vector.ipynb

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    "# A Glimpse of Daru::Vector\n",
    "\n",
    "In [daru](https://github.com/v0dro/daru), the Daru::Vector is a 1 dimensional array with axis labels.\n",
    "\n",
    "Labels should be unique. The object supports both integer- and label-based indexing and provides a host of methods for performing operations involving the index. Statistical methods automatically exclude missing data (currently represented by default as nil).\n",
    "\n",
    "Operations between Vectors (+, -, /, , \\*) align values based on their associated index values. The Vectors need not be of similar length. The result index will be the sorted union of the two indexes.\n",
    "\n",
    "Daru::Vector is similar to pandas.Series."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The examples below demonstrates how a simple Daru::Vector can be created and its data viewed.\n",
    "\n",
    "This first example shows very basic creation of a Vector with missing data (represented by *nil*)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
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   "source": [
    "require 'daru'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The very basic way to create a Vector is by just passing an Array of values into the constructor.\n",
    "\n",
    "Index labels can be specified using the `:index` option and you can also name your Vector something using the `:name` option. In case `:index` isn't specified, the Vector will be assigned an index starting from 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
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     "data": {
      "text/html": [
       "<table><tr><th colspan=\"2\">Daru::Vector:30420060  size: 5</th></tr><tr><th> </th><th>bazinga</th></tr><tr><td>a</td><td>1</td></tr><tr><td>b</td><td>2</td></tr><tr><td>c</td><td>3</td></tr><tr><td>d</td><td>4</td></tr><tr><td>e</td><td>5</td></tr></table>"
      ],
      "text/plain": [
       "\n",
       "#<Daru::Vector:30420060 @name = bazinga @size = 5 >\n",
       "        bazinga\n",
       "      a       1\n",
       "      b       2\n",
       "      c       3\n",
       "      d       4\n",
       "      e       5\n"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "a = Daru::Vector.new([1,2,3,4,5], index: [:a, :b, :c, :d, :e], name: :bazinga)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Values can be accessed using their labels with the `#[]` operator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
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       "2"
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     "execution_count": 3,
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   ],
   "source": [
    "a[:b]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "OR you can even specify a range with labels..."
   ]
  },
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   "cell_type": "code",
   "execution_count": 4,
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     "data": {
      "text/html": [
       "<table><tr><th colspan=\"2\">Daru::Vector:29850660  size: 3</th></tr><tr><th> </th><th>bazinga</th></tr><tr><td>b</td><td>2</td></tr><tr><td>c</td><td>3</td></tr><tr><td>d</td><td>4</td></tr></table>"
      ],
      "text/plain": [
       "\n",
       "#<Daru::Vector:29850660 @name = bazinga @size = 3 >\n",
       "        bazinga\n",
       "      b       2\n",
       "      c       3\n",
       "      d       4\n"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "a[:b..:d]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Values can be assigned with the `#[]=` operator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
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    {
     "data": {
      "text/html": [
       "<table><tr><th colspan=\"2\">Daru::Vector:30420060  size: 5</th></tr><tr><th> </th><th>bazinga</th></tr><tr><td>a</td><td>1</td></tr><tr><td>b</td><td>999</td></tr><tr><td>c</td><td>3</td></tr><tr><td>d</td><td>4</td></tr><tr><td>e</td><td>5</td></tr></table>"
      ],
      "text/plain": [
       "\n",
       "#<Daru::Vector:30420060 @name = bazinga @size = 5 >\n",
       "        bazinga\n",
       "      a       1\n",
       "      b     999\n",
       "      c       3\n",
       "      d       4\n",
       "      e       5\n"
      ]
     },
     "execution_count": 5,
     "metadata": {},
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   "source": [
    "a[:b] = 999\n",
    "a"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you want to treat values apart from *nil* as missing, you can specify them using the `:missing_values` option.\n",
    "\n",
    "The `#only_valid` method can then be used for obtaining all the *non-missing* values of the Vector. Notice that `only_valid` preserves the indexes (labels) of the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
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   "outputs": [
    {
     "data": {
      "text/html": [
       "<table><tr><th colspan=\"2\">Daru::Vector:29284260  size: 5</th></tr><tr><th> </th><th>nil</th></tr><tr><td>0</td><td>1</td></tr><tr><td>1</td><td>2</td></tr><tr><td>2</td><td>3</td></tr><tr><td>5</td><td>4</td></tr><tr><td>6</td><td>6</td></tr></table>"
      ],
      "text/plain": [
       "\n",
       "#<Daru::Vector:29284260 @name = nil @size = 5 >\n",
       "    nil\n",
       "  0   1\n",
       "  1   2\n",
       "  2   3\n",
       "  5   4\n",
       "  6   6\n"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = Daru::Vector.new([1,2,3,5,5,4,6,nil,nil], missing_values: [5,nil])\n",
    "a.only_valid"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `Vector.[]` class method creates a vector from almost any object that has a `#to_a` method defined on it. It is similar to R's `c` method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "data": {
      "text/html": [
       "<table><tr><th colspan=\"2\">Daru::Vector:28825140  size: 9</th></tr><tr><th> </th><th>nil</th></tr><tr><td>0</td><td>1</td></tr><tr><td>1</td><td>2</td></tr><tr><td>2</td><td>3</td></tr><tr><td>3</td><td>4</td></tr><tr><td>4</td><td>6</td></tr><tr><td>5</td><td>7</td></tr><tr><td>6</td><td>8</td></tr><tr><td>7</td><td>9</td></tr><tr><td>8</td><td>10</td></tr></table>"
      ],
      "text/plain": [
       "\n",
       "#<Daru::Vector:28825140 @name = nil @size = 9 >\n",
       "    nil\n",
       "  0   1\n",
       "  1   2\n",
       "  2   3\n",
       "  3   4\n",
       "  4   6\n",
       "  5   7\n",
       "  6   8\n",
       "  7   9\n",
       "  8  10\n"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = Daru::Vector[1,2,3,4,6..10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The *new_with_size* class method lets you create a Daru::Vector by specifying the size as the argument. The optional block, if supplied, is run once for populating each element in the Vector.\n",
    "\n",
    "The result of each run of the block is the value that is ultimately assigned to that position in the Vector."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table><tr><th colspan=\"2\">Daru::Vector:28500640  size: 1000</th></tr><tr><th> </th><th>new_vector</th></tr><tr><td>0</td><td>2</td></tr><tr><td>1</td><td>3</td></tr><tr><td>2</td><td>0</td></tr><tr><td>3</td><td></td></tr><tr><td>4</td><td></td></tr><tr><td>5</td><td>2</td></tr><tr><td>6</td><td>2</td></tr><tr><td>7</td><td>2</td></tr><tr><td>8</td><td>1</td></tr><tr><td>9</td><td>1</td></tr><tr><td>10</td><td>3</td></tr><tr><td>11</td><td>0</td></tr><tr><td>12</td><td>2</td></tr><tr><td>13</td><td>0</td></tr><tr><td>14</td><td>3</td></tr><tr><td>15</td><td>1</td></tr><tr><td>16</td><td>3</td></tr><tr><td>17</td><td>1</td></tr><tr><td>18</td><td>3</td></tr><tr><td>19</td><td>0</td></tr><tr><td>20</td><td>1</td></tr><tr><td>21</td><td>1</td></tr><tr><td>22</td><td>2</td></tr><tr><td>23</td><td>2</td></tr><tr><td>24</td><td>2</td></tr><tr><td>25</td><td>3</td></tr><tr><td>26</td><td>3</td></tr><tr><td>27</td><td>2</td></tr><tr><td>28</td><td>0</td></tr><tr><td>29</td><td></td></tr><tr><td>30</td><td>3</td></tr><tr><td>31</td><td>3</td></tr><tr><td>...</td><td>...</td></tr><tr><td>999</td><td>3</td></tr></table>"
      ],
      "text/plain": [
       "\n",
       "#<Daru::Vector:28500640 @name = new_vector @size = 1000 >\n",
       "           new_vector\n",
       "         0          2\n",
       "         1          3\n",
       "         2          0\n",
       "         3        nil\n",
       "         4        nil\n",
       "         5          2\n",
       "         6          2\n",
       "         7          2\n",
       "         8          1\n",
       "         9          1\n",
       "        10          3\n",
       "        11          0\n",
       "        12          2\n",
       "        13          0\n",
       "        14          3\n",
       "        15          1\n",
       "        16          3\n",
       "       ...        ...\n"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = Daru::Vector.new_with_size(1000, name: :new_vector) { r=rand(5); r == 4 ? nil: r; }"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use the `#head` method for obtaining the top 10 values of the Vector."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table><tr><th colspan=\"2\">Daru::Vector:27175540  size: 10</th></tr><tr><th> </th><th>new_vector</th></tr><tr><td>0</td><td>2</td></tr><tr><td>1</td><td>3</td></tr><tr><td>2</td><td>0</td></tr><tr><td>3</td><td></td></tr><tr><td>4</td><td></td></tr><tr><td>5</td><td>2</td></tr><tr><td>6</td><td>2</td></tr><tr><td>7</td><td>2</td></tr><tr><td>8</td><td>1</td></tr><tr><td>9</td><td>1</td></tr></table>"
      ],
      "text/plain": [
       "\n",
       "#<Daru::Vector:27175540 @name = new_vector @size = 10 >\n",
       "           new_vector\n",
       "         0          2\n",
       "         1          3\n",
       "         2          0\n",
       "         3        nil\n",
       "         4        nil\n",
       "         5          2\n",
       "         6          2\n",
       "         7          2\n",
       "         8          1\n",
       "         9          1\n"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.head"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sorting\n",
    "\n",
    "The `Daru::Vector#sort` method will sort the Vector and preserve the indexes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table><tr><th colspan=\"2\">Daru::Vector:25317760  size: 8</th></tr><tr><th> </th><th>nil</th></tr><tr><td>0</td><td>23</td></tr><tr><td>1</td><td>144</td></tr><tr><td>2</td><td>332</td></tr><tr><td>3</td><td>11</td></tr><tr><td>4</td><td>2</td></tr><tr><td>5</td><td>5</td></tr><tr><td>6</td><td>6765</td></tr><tr><td>7</td><td>3</td></tr></table>"
      ],
      "text/plain": [
       "\n",
       "#<Daru::Vector:25317760 @name = nil @size = 8 >\n",
       "      nil\n",
       "   0   23\n",
       "   1  144\n",
       "   2  332\n",
       "   3   11\n",
       "   4    2\n",
       "   5    5\n",
       "   6 6765\n",
       "   7    3\n"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = Daru::Vector.new([23,144,332,11,2,5,6765,3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
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    {
     "data": {
      "text/html": [
       "<table><tr><th colspan=\"2\">Daru::Vector:24840120  size: 8</th></tr><tr><th> </th><th>nil</th></tr><tr><td>4</td><td>2</td></tr><tr><td>7</td><td>3</td></tr><tr><td>5</td><td>5</td></tr><tr><td>3</td><td>11</td></tr><tr><td>0</td><td>23</td></tr><tr><td>1</td><td>144</td></tr><tr><td>2</td><td>332</td></tr><tr><td>6</td><td>6765</td></tr></table>"
      ],
      "text/plain": [
       "\n",
       "#<Daru::Vector:24840120 @name = nil @size = 8 >\n",
       "      nil\n",
       "   4    2\n",
       "   7    3\n",
       "   5    5\n",
       "   3   11\n",
       "   0   23\n",
       "   1  144\n",
       "   2  332\n",
       "   6 6765\n"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.sort"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Basic Math\n",
    "\n",
    "Arithmetic operations done between two vectors will always perform the arithmetic on corresponding elements of the same index.\n",
    "\n",
    "The concerned vectors need not have the same size of even the same index. In case of a mismatch, a sorted union of the indexes of both the Vectors is used as an index for the resulting vector.\n",
    "\n",
    "In case a particular index exists in one vector but not in the other, the result Vector has a *nil* placed in that index position.\n",
    "\n",
    "Daru::Vector supports +, -, \\*, / and \\*\\* operators."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table><tr><th colspan=\"2\">Daru::Vector:24525720  size: 7</th></tr><tr><th> </th><th>nil</th></tr><tr><td>a</td><td>2</td></tr><tr><td>b</td><td>4</td></tr><tr><td>c</td><td>6</td></tr><tr><td>d</td><td></td></tr><tr><td>f</td><td></td></tr><tr><td>ff</td><td></td></tr><tr><td>five</td><td>10</td></tr></table>"
      ],
      "text/plain": [
       "\n",
       "#<Daru::Vector:24525720 @name = nil @size = 7 >\n",
       "      nil\n",
       "   a    2\n",
       "   b    4\n",
       "   c    6\n",
       "   d  nil\n",
       "   f  nil\n",
       "  ff  nil\n",
       "five   10\n"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = Daru::Vector.new([1,2,3,4,5,6], index: [:a, :b, :c, :d, :five, :f])\n",
    "b = Daru::Vector.new([1,2,3,4,5], index: [:a, :b, :c, :ff,:five])\n",
    "\n",
    "a + b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "data": {
      "text/html": [
       "<table><tr><th colspan=\"2\">Daru::Vector:24243560  size: 7</th></tr><tr><th> </th><th>nil</th></tr><tr><td>a</td><td>1</td></tr><tr><td>b</td><td>4</td></tr><tr><td>c</td><td>27</td></tr><tr><td>d</td><td></td></tr><tr><td>f</td><td></td></tr><tr><td>ff</td><td></td></tr><tr><td>five</td><td>3125</td></tr></table>"
      ],
      "text/plain": [
       "\n",
       "#<Daru::Vector:24243560 @name = nil @size = 7 >\n",
       "      nil\n",
       "   a    1\n",
       "   b    4\n",
       "   c   27\n",
       "   d  nil\n",
       "   f  nil\n",
       "  ff  nil\n",
       "five 3125\n"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a ** b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Performing arithmetic with a single number will perform the operation on each element in the Vector and return the resultant Vector."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table><tr><th colspan=\"2\">Daru::Vector:23813900  size: 6</th></tr><tr><th> </th><th>nil</th></tr><tr><td>a</td><td>5</td></tr><tr><td>b</td><td>10</td></tr><tr><td>c</td><td>15</td></tr><tr><td>d</td><td>20</td></tr><tr><td>five</td><td>25</td></tr><tr><td>f</td><td>30</td></tr></table>"
      ],
      "text/plain": [
       "\n",
       "#<Daru::Vector:23813900 @name = nil @size = 6 >\n",
       "      nil\n",
       "   a    5\n",
       "   b   10\n",
       "   c   15\n",
       "   d   20\n",
       "five   25\n",
       "   f   30\n"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a * 5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Statistics\n",
    "\n",
    "Daru::Vector defines a host of statistics methods, which are useful for performing ephemeral statistics on numeric data. All the statistics methods ignore the *missing* values and work only on the valid data.\n",
    "\n",
    "For a complete list of statistics functions see the Daru::Maths::Statistics::Vector module in the [docs](https://rubygems.org/gems/daru)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.0"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v = Daru::Vector.new([1,2,3,4,5,nil,6,nil,7])\n",
    "v.mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.666666666666667"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v.variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v.median"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting\n",
    "\n",
    "Daru uses [nyaplot](https://github.com/domitry/nyaplot/tree/master) internally for generating interactive plots.\n",
    "\n",
    "You can also use rubyvis through [statsample](https://github.com/SciRuby/statsample) for quickly generating scatter plots, histograms and box plots."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A simple scatter plot can be generated by simply calling the `#plot` function on Daru::Vector. Feel free to interact with the generated plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div id='vis-e805a0f4-5755-4c99-a214-71e722969479'></div>\n",
       "<script>\n",
       "(function(){\n",
       "    var render = function(){\n",
       "        var model = {\"panes\":[{\"diagrams\":[{\"type\":\"scatter\",\"options\":{\"x\":\"data0\",\"y\":\"data1\"},\"data\":\"af343b05-60ad-4c07-8d00-8fbfb77c0e4c\"}],\"options\":{\"zoom\":true,\"width\":700,\"xrange\":[0,51],\"yrange\":[-0.9986295347545738,0.9998476951563913]}}],\"data\":{\"af343b05-60ad-4c07-8d00-8fbfb77c0e4c\":[{\"data0\":0,\"data1\":0.0},{\"data0\":1,\"data1\":0.12186934340514748},{\"data0\":2,\"data1\":0.24192189559966773},{\"data0\":3,\"data1\":0.35836794954530027},{\"data0\":4,\"data1\":0.4694715627858908},{\"data0\":5,\"data1\":0.573576436351046},{\"data0\":6,\"data1\":0.6691306063588582},{\"data0\":7,\"data1\":0.754709580222772},{\"data0\":8,\"data1\":0.8290375725550417},{\"data0\":9,\"data1\":0.8910065241883678},{\"data0\":10,\"data1\":0.9396926207859083},{\"data0\":11,\"data1\":0.9743700647852352},{\"data0\":12,\"data1\":0.9945218953682733},{\"data0\":13,\"data1\":0.9998476951563913},{\"data0\":14,\"data1\":0.9902680687415704},{\"data0\":15,\"data1\":0.9659258262890683},{\"data0\":16,\"data1\":0.9271838545667874},{\"data0\":17,\"data1\":0.8746197071393959},{\"data0\":18,\"data1\":0.8090169943749475},{\"data0\":19,\"data1\":0.7313537016191706},{\"data0\":20,\"data1\":0.6427876096865395},{\"data0\":21,\"data1\":0.544639035015027},{\"data0\":22,\"data1\":0.4383711467890773},{\"data0\":23,\"data1\":0.32556815445715703},{\"data0\":24,\"data1\":0.20791169081775931},{\"data0\":25,\"data1\":0.08715574274765864},{\"data0\":26,\"data1\":-0.0348994967025009},{\"data0\":27,\"data1\":-0.15643446504023073},{\"data0\":28,\"data1\":-0.275637355816999},{\"data0\":29,\"data1\":-0.39073112848927355},{\"data0\":30,\"data1\":-0.5000000000000001},{\"data0\":31,\"data1\":-0.601815023152048},{\"data0\":32,\"data1\":-0.6946583704589974},{\"data0\":33,\"data1\":-0.7771459614569711},{\"data0\":34,\"data1\":-0.848048096156426},{\"data0\":35,\"data1\":-0.9063077870366497},{\"data0\":36,\"data1\":-0.9510565162951535},{\"data0\":37,\"data1\":-0.9816271834476639},{\"data0\":38,\"data1\":-0.9975640502598242},{\"data0\":39,\"data1\":-0.9986295347545738},{\"data0\":40,\"data1\":-0.9848077530122081},{\"data0\":41,\"data1\":-0.9563047559630354},{\"data0\":42,\"data1\":-0.9135454576426008},{\"data0\":43,\"data1\":-0.8571673007021123},{\"data0\":44,\"data1\":-0.7880107536067218},{\"data0\":45,\"data1\":-0.7071067811865477},{\"data0\":46,\"data1\":-0.6156614753256588},{\"data0\":47,\"data1\":-0.5150380749100545},{\"data0\":48,\"data1\":-0.40673664307580015},{\"data0\":49,\"data1\":-0.29237170472273627},{\"data0\":50,\"data1\":-0.17364817766693127},{\"data0\":51,\"data1\":-0.05233595624294437}]},\"extension\":[]}\n",
       "        var id_name = '#vis-e805a0f4-5755-4c99-a214-71e722969479';\n",
       "        Nyaplot.core.parse(model, id_name);\n",
       "\n",
       "        require(['downloadable'], function(downloadable){\n",
       "          var svg = d3.select(id_name).select(\"svg\");\n",
       "\t  if(!svg.empty())\n",
       "\t    svg.call(downloadable().filename('fig'));\n",
       "\t});\n",
       "    };\n",
       "    if(window['Nyaplot']==undefined){\n",
       "        window.addEventListener('load_nyaplot', render, false);\n",
       "\treturn;\n",
       "    } else {\n",
       "       render();\n",
       "    }\n",
       "})();\n",
       "</script>\n"
      ],
      "text/plain": [
       "#<Nyaplot::Frame:0x000000028e17a8 @properties={:panes=>[#<Nyaplot::Plot:0x000000028f2e68 @properties={:diagrams=>[#<Nyaplot::Diagram:0x000000028e1dc0 @properties={:type=>:scatter, :options=>{:x=>\"data0\", :y=>\"data1\"}, :data=>\"af343b05-60ad-4c07-8d00-8fbfb77c0e4c\"}, @xrange=[0, 51], @yrange=[-0.9986295347545738, 0.9998476951563913]>], :options=>{:zoom=>true, :width=>700, :xrange=>[0, 51], :yrange=>[-0.9986295347545738, 0.9998476951563913]}}>], :data=>{\"af343b05-60ad-4c07-8d00-8fbfb77c0e4c\"=>#<Nyaplot::DataFrame:0x000000028f26c0 @name=\"af343b05-60ad-4c07-8d00-8fbfb77c0e4c\", @rows=[{:data0=>0, :data1=>0.0}, {:data0=>1, :data1=>0.12186934340514748}, {:data0=>2, :data1=>0.24192189559966773}, {:data0=>3, :data1=>0.35836794954530027}, {:data0=>4, :data1=>0.4694715627858908}, {:data0=>5, :data1=>0.573576436351046}, {:data0=>6, :data1=>0.6691306063588582}, {:data0=>7, :data1=>0.754709580222772}, {:data0=>8, :data1=>0.8290375725550417}, {:data0=>9, :data1=>0.8910065241883678}, {:data0=>10, :data1=>0.9396926207859083}, {:data0=>11, :data1=>0.9743700647852352}, {:data0=>12, :data1=>0.9945218953682733}, {:data0=>13, :data1=>0.9998476951563913}, {:data0=>14, :data1=>0.9902680687415704}, {:data0=>15, :data1=>0.9659258262890683}, {:data0=>16, :data1=>0.9271838545667874}, {:data0=>17, :data1=>0.8746197071393959}, {:data0=>18, :data1=>0.8090169943749475}, {:data0=>19, :data1=>0.7313537016191706}, {:data0=>20, :data1=>0.6427876096865395}, {:data0=>21, :data1=>0.544639035015027}, {:data0=>22, :data1=>0.4383711467890773}, {:data0=>23, :data1=>0.32556815445715703}, {:data0=>24, :data1=>0.20791169081775931}, {:data0=>25, :data1=>0.08715574274765864}, {:data0=>26, :data1=>-0.0348994967025009}, {:data0=>27, :data1=>-0.15643446504023073}, {:data0=>28, :data1=>-0.275637355816999}, {:data0=>29, :data1=>-0.39073112848927355}, {:data0=>30, :data1=>-0.5000000000000001}, {:data0=>31, :data1=>-0.601815023152048}, {:data0=>32, :data1=>-0.6946583704589974}, {:data0=>33, :data1=>-0.7771459614569711}, {:data0=>34, :data1=>-0.848048096156426}, {:data0=>35, :data1=>-0.9063077870366497}, {:data0=>36, :data1=>-0.9510565162951535}, {:data0=>37, :data1=>-0.9816271834476639}, {:data0=>38, :data1=>-0.9975640502598242}, {:data0=>39, :data1=>-0.9986295347545738}, {:data0=>40, :data1=>-0.9848077530122081}, {:data0=>41, :data1=>-0.9563047559630354}, {:data0=>42, :data1=>-0.9135454576426008}, {:data0=>43, :data1=>-0.8571673007021123}, {:data0=>44, :data1=>-0.7880107536067218}, {:data0=>45, :data1=>-0.7071067811865477}, {:data0=>46, :data1=>-0.6156614753256588}, {:data0=>47, :data1=>-0.5150380749100545}, {:data0=>48, :data1=>-0.40673664307580015}, {:data0=>49, :data1=>-0.29237170472273627}, {:data0=>50, :data1=>-0.17364817766693127}, {:data0=>51, :data1=>-0.05233595624294437}]>}, :extension=>[]}>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "v = Daru::Vector.new((0..360).step(7).map { |i| Math.sin((i*Math::PI)/180) })\n",
    "v.plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, lets take some dummy data of a survey that shows the number of people of each age group that are part of this survey. We want to plot the number of people from each age group who have taken the test in a bar graph.\n",
    "\n",
    "For this purpose we use the `#plot` function again, but this time supply it with the `:type` option, and set the value of this option as `:bar`. The plot function yeilds the corresponding `Nyaplot::Plot` object in the block, which can then be used for setting different parameters of the final plot. For more configuration methods see the [Nyaplot::Plot](https://rubygems.org/gems/nyaplot) documentation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div id='vis-d0366230-5fc7-42f3-9020-71c393f440a8'></div>\n",
       "<script>\n",
       "(function(){\n",
       "    var render = function(){\n",
       "        var model = {\"panes\":[{\"diagrams\":[{\"type\":\"bar\",\"options\":{\"x\":\"data0\",\"y\":\"data1\"},\"data\":\"14350137-a098-4569-b38d-25cad4745a72\"}],\"options\":{\"x_label\":\"Age Groups\",\"y_label\":\"Number of People Surveyed\",\"width\":700,\"xrange\":[\"18-24\",\"24-30\",\"Under 18\",\"30-40\",\"40-50\"],\"yrange\":[0,70]}}],\"data\":{\"14350137-a098-4569-b38d-25cad4745a72\":[{\"data0\":\"18-24\",\"data1\":40},{\"data0\":\"24-30\",\"data1\":50},{\"data0\":\"Under 18\",\"data1\":20},{\"data0\":\"30-40\",\"data1\":70},{\"data0\":\"40-50\",\"data1\":10}]},\"extension\":[]}\n",
       "        var id_name = '#vis-d0366230-5fc7-42f3-9020-71c393f440a8';\n",
       "        Nyaplot.core.parse(model, id_name);\n",
       "\n",
       "        require(['downloadable'], function(downloadable){\n",
       "          var svg = d3.select(id_name).select(\"svg\");\n",
       "\t  if(!svg.empty())\n",
       "\t    svg.call(downloadable().filename('fig'));\n",
       "\t});\n",
       "    };\n",
       "    if(window['Nyaplot']==undefined){\n",
       "        window.addEventListener('load_nyaplot', render, false);\n",
       "\treturn;\n",
       "    } else {\n",
       "       render();\n",
       "    }\n",
       "})();\n",
       "</script>\n"
      ],
      "text/plain": [
       "#<Nyaplot::Frame:0x0000000286d420 @properties={:panes=>[#<Nyaplot::Plot:0x0000000286ea78 @properties={:diagrams=>[#<Nyaplot::Diagram:0x0000000286da38 @properties={:type=>:bar, :options=>{:x=>\"data0\", :y=>\"data1\"}, :data=>\"14350137-a098-4569-b38d-25cad4745a72\"}, @xrange=[\"18-24\", \"24-30\", \"Under 18\", \"30-40\", \"40-50\"], @yrange=[0, 70]>], :options=>{:x_label=>\"Age Groups\", :y_label=>\"Number of People Surveyed\", :width=>700, :xrange=>[\"18-24\", \"24-30\", \"Under 18\", \"30-40\", \"40-50\"], :yrange=>[0, 70]}}>], :data=>{\"14350137-a098-4569-b38d-25cad4745a72\"=>#<Nyaplot::DataFrame:0x0000000286e488 @name=\"14350137-a098-4569-b38d-25cad4745a72\", @rows=[{:data0=>\"18-24\", :data1=>40}, {:data0=>\"24-30\", :data1=>50}, {:data0=>\"Under 18\", :data1=>20}, {:data0=>\"30-40\", :data1=>70}, {:data0=>\"40-50\", :data1=>10}]>}, :extension=>[]}>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "v = Daru::Vector.new([40,50,20,70,10], index: ['18-24', '24-30', 'Under 18', '30-40', '40-50'], name: \"Age Range\")\n",
    "v.plot(type: :bar) do |plt|\n",
    "  plt.x_label \"Age Groups\"\n",
    "  plt.y_label \"Number of People Surveyed\"\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The third kind of plot that Daru::Vector can easily generate from nyaplot is the histogram.\n",
    "\n",
    "To demonstrate, we'll prepare some sample data using the `rnorm` function from the `statsample` ruby gem. The rnorm function just generates normally distributied random variables (1000 in this case) and returns a Daru::Vector object that contains these numbers (in variable `a`).\n",
    "\n",
    "A histogram of the normally distributed function has been generated below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div id='vis-a28dcc05-d55a-4696-b0aa-539a1bddbaa6'></div>\n",
       "<script>\n",
       "(function(){\n",
       "    var render = function(){\n",
       "        var model = 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       "        var id_name = '#vis-a28dcc05-d55a-4696-b0aa-539a1bddbaa6';\n",
       "        Nyaplot.core.parse(model, id_name);\n",
       "\n",
       "        require(['downloadable'], function(downloadable){\n",
       "          var svg = d3.select(id_name).select(\"svg\");\n",
       "\t  if(!svg.empty())\n",
       "\t    svg.call(downloadable().filename('fig'));\n",
       "\t});\n",
       "    };\n",
       "    if(window['Nyaplot']==undefined){\n",
       "        window.addEventListener('load_nyaplot', render, false);\n",
       "\treturn;\n",
       "    } else {\n",
       "       render();\n",
       "    }\n",
       "})();\n",
       "</script>\n"
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "require 'statsample'\n",
    "include Statsample::Shorthand\n",
    "\n",
    "a = rnorm(1000)\n",
    "a.plot type: :histogram do |p|\n",
    "  p.yrange [0,200]\n",
    "  p.y_label \"Frequency\"\n",
    "  p.x_label \"Bins\"\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### More plotting support\n",
    "\n",
    "Apart from interfacing with nyaplot, Daru::Vector also works out-of-the-box with rubyvis through statsample. To see generating plots with statsample and rubyvis in action, checkout the following notebooks:\n",
    "\n",
    "* [Histogram](http://nbviewer.ipython.org/github/SciRuby/sciruby-notebooks/blob/master/Visualization/Creating%20a%20Histogram.ipynb)\n",
    "* [Scatter Plot](http://nbviewer.ipython.org/github/SciRuby/sciruby-notebooks/blob/master/Visualization/Scatterplot%20with%20statsample.ipynb)\n",
    "* [Box Plot](http://nbviewer.ipython.org/github/SciRuby/sciruby-notebooks/blob/master/Visualization/Boxplot%20with%20daru%20and%20statsample.ipynb)"
   ]
  }
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