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<title>PyXPlot Users' Guide: Time Intervals</title>

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<b class="current">Time Intervals</b>
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<div><h2 id="a0000000026">4.11.1 Time Intervals</h2>
<p>Two functions are provided for measuring the time intervals elapsed between pairs of Julian Day numbers. These are useful when an experiment is started at some time <img src="images/img-0019.png" alt="$x$" style="vertical-align:0px; 
                                     width:10px; 
                                     height:8px" class="math gen" />, and datapoints are to be labelled with the times elapsed since the beginning of the experiment. The <tt class="tt">time_diff()</tt> function<a name="a0000000496" id="a0000000496"></a> returns the time interval, with physical dimensions of time, between two Julian Day numbers. This function is actually very simple, and is entirely equivalent to the algebraic expression <tt class="tt">(y-x)*unit(day)</tt>. The following example, demonstrates its use to calculate the time elapsed between the traditional date for the foundation of Rome by Romulus and Remus in 753 <small class="footnotesize">BC</small> and that of the deposition of the last Emperor of the Western Empire in <small class="footnotesize">AD</small> 476: </p><p> <tt class="tt">pyxplot&gt; <b class="bf">x = time_julianday(-752,4,21,12,0,0)</b></tt><br /><tt class="tt">pyxplot&gt; <b class="bf">y = time_julianday( 476,9, 4,12,0,0)</b></tt><br /><tt class="tt">pyxplot&gt; <b class="bf">print time_diff(x,y)</b></tt><br /><tt class="tt">3.8764483e+10 s</tt><br /><tt class="tt">pyxplot&gt; <b class="bf">print time_diff(x,y)/unit(year)</b></tt><br /><tt class="tt">1228.3723</tt>  </p><p>The function <tt class="tt">time_diff_string()</tt><a name="a0000000497" id="a0000000497"></a> is similar, but returns a textual representation of the time interval, and is useful for producing textual axis labels representing the time elapsed since the beginning of an experiment. As with the <tt class="tt">time_string()</tt> function, it takes an optional third parameter which specifies the textual format in which the time interval should be represented. If no format is supplied, then the following verbose format is used:<br /><tt class="tt">"%Y years %d days %h hours %m minutes and %s seconds"</tt><br />Table <a href="sect0025.html#ex:timeseries">4.4</a> lists the tokens which are substituted for various parts of the time interval. The following examples demonstrate the use of the function: </p><div id="ex:timeseries" class="table"><center> <table cellspacing="0" class="tabular">
<tr>

    
    <td style="border-top-style:solid; border-left:1px solid black; border-right:1px solid black; border-top-color:black; border-top-width:1px; text-align:left"><p> Token </p></td>

    
    <td style="border-top-style:solid; text-align:left; border-top-color:black; border-top-width:1px; border-right:1px solid black"><p> Substitution value </p></td>

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    <td style="border-top-style:solid; border-left:1px solid black; border-right:1px solid black; border-top-color:black; border-top-width:1px; text-align:left"><p><tt class="tt">%%</tt> </p></td>

    
    <td style="border-top-style:solid; text-align:left; border-top-color:black; border-top-width:1px; border-right:1px solid black"><p> A literal % sign.</p></td>

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    <td style="text-align:left; border-right:1px solid black; border-left:1px solid black"><p><tt class="tt">%d</tt> </p></td>

    
    <td style="text-align:left; border-right:1px solid black"><p> The number of days elapsed, modulo 365.</p></td>

</tr><tr>

    
    <td style="text-align:left; border-right:1px solid black; border-left:1px solid black"><p><tt class="tt">%D</tt> </p></td>

    
    <td style="text-align:left; border-right:1px solid black"><p> The number of days elapsed. </p></td>

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    <td style="text-align:left; border-right:1px solid black; border-left:1px solid black"><p><tt class="tt">%h</tt> </p></td>

    
    <td style="text-align:left; border-right:1px solid black"><p> The number of hours elapsed, modulo 24.</p></td>

</tr><tr>

    
    <td style="text-align:left; border-right:1px solid black; border-left:1px solid black"><p><tt class="tt">%H</tt> </p></td>

    
    <td style="text-align:left; border-right:1px solid black"><p> The number of hours elapsed.</p></td>

</tr><tr>

    
    <td style="text-align:left; border-right:1px solid black; border-left:1px solid black"><p><tt class="tt">%m</tt> </p></td>

    
    <td style="text-align:left; border-right:1px solid black"><p> The number of minutes elapsed, modulo 60.</p></td>

</tr><tr>

    
    <td style="text-align:left; border-right:1px solid black; border-left:1px solid black"><p><tt class="tt">%M</tt> </p></td>

    
    <td style="text-align:left; border-right:1px solid black"><p> The number of minutes elapsed.</p></td>

</tr><tr>

    
    <td style="text-align:left; border-right:1px solid black; border-left:1px solid black"><p><tt class="tt">%s</tt> </p></td>

    
    <td style="text-align:left; border-right:1px solid black"><p> The number of seconds elapsed, modulo 60.</p></td>

</tr><tr>

    
    <td style="text-align:left; border-right:1px solid black; border-left:1px solid black"><p><tt class="tt">%S</tt> </p></td>

    
    <td style="text-align:left; border-right:1px solid black"><p> The number of seconds elapsed.</p></td>

</tr><tr>

    
    <td style="border-bottom-style:solid; border-bottom-width:1px; border-left:1px solid black; border-right:1px solid black; text-align:left; border-bottom-color:black"><p><tt class="tt">%Y</tt> </p></td>

    
    <td style="border-bottom-color:black; border-bottom-width:1px; text-align:left; border-bottom-style:solid; border-right:1px solid black"><p> The number of years elapsed.</p></td>

</tr>
</table> </center><div class="caption"><b>Table 4.4</b>: <span>Tokens which are substituted for various components of the time interval by the <tt class="tt">time_diff_string</tt> function.</span></div></div><p> <tt class="tt">pyxplot&gt; <b class="bf">x = time_julianday(-752,4,21,12,0,0)</b></tt><br /><tt class="tt">pyxplot&gt; <b class="bf">y = time_julianday( 476,9, 4,12,0,0)</b></tt><br /><tt class="tt">pyxplot&gt; <b class="bf">print time_diff_string(x,y)</b></tt><br /><tt class="tt">1229 years 78 days 0 hours 0 minutes and 0 seconds</tt><br /><tt class="tt">pyxplot&gt; <b class="bf">print time_diff_string(x,y,"$%Y<img src="images/img-0024.png" alt="\^{}" style="vertical-align:9px; width:5px; height:4px" class="accent gen" /><img src="images/img-0006.png" alt="$\backslash $" style="vertical-align:-5px; 
                                     width:7px; 
                                     height:18px" class="math gen" />mathrm{y}%d<img src="images/img-0024.png" alt="\^{}" style="vertical-align:9px; width:5px; height:4px" class="accent gen" /><img src="images/img-0006.png" alt="$\backslash $" style="vertical-align:-5px; 
                                     width:7px; 
                                     height:18px" class="math gen" />mathrm{d}$")</b></tt><br /><tt class="tt"><img src="images/img-0159.png" alt="$1229^\mathrm {y}78^\mathrm {d}$" style="vertical-align:0px; 
                                     width:69px; 
                                     height:17px" class="math gen" /></tt>  </p><p> <span class="upshape"><span class="mdseries"><span class="rm">A plot of the rate of downloads from an Apache webserver.</span></span></span></p><div>

<table cellspacing="0" class="tabular">
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    <td style="border-top-style:solid; border-left:1px solid black; border-right:1px solid black; border-top-color:black; border-top-width:1px; text-align:left"><p> In this example, we use PyXPlot’s facilities for handling dates and times to produce a plot of the rate of downloads from an Apache webserver based upon the download log which it stores in the file <tt class="tt">/var/log/apache2/access.log</tt>. This file contain a line of the following form for each page or file requested from the webserver: <br /><tt class="tt"><small class="footnotesize">127.0.0.1 - - [14/Apr/2010:16:05:36 +0100] "GET / HTTP/1.1" 200 2623 "-" "Mozilla/5.0 (X11; U; Linux x86_64; en-GB; rv:1.9.1.9) Gecko/20100402 Ubuntu/9.10 (karmic) Firefox/3.5.9"</small></tt><br />However, PyXPlot’s default input filter for <tt class="tt">.log</tt> files (see Section <a href="sec-filters.html">5.1</a>) manipulates the dates in strings such as these into the form <br /><tt class="tt"><small class="footnotesize">127.0.0.1 - -  [ 14  4  2010 16 05 36 +0100 ]  "GET   HTTP 1.1" 200 2623 "-" "Mozilla 5.0 (X11; U; Linux x86_64; en-GB; rv 1.9.1.9) Gecko 20100402 Ubuntu 9.10 (karmic) Firefox 3.5.9"</small></tt><br />such that the day, month, year, hour, minute and second components of the date are contained in the 5th to 10th white-space-separated columns respectively. In the script below, the <tt class="tt">time_­julianday()</tt> is then used to convert these components into Julian Days, and the <tt class="tt">histogram</tt> command<a name="a0000000498" id="a0000000498"></a> (see Section <a href="sec-histogram.html">5.9</a>) is used to sort each of the web accesses recorded in the Apache log file into hour-sized bins. Because this may be a time-consuming process for large log files on busy servers, we use the <tt class="tt">tabulate</tt> command<a name="a0000000499" id="a0000000499"></a> (see Section <a href="sec-tabulate.html">5.5</a>) to store the data into a temporary datafile on disk before deciding how to plot it: </p></td>

</tr><tr>

    
    <td style="text-align:left; border-right:1px solid black; border-left:1px solid black"><p><tt class="tt">set output ’apache.dat’</tt><br /><tt class="tt">histogram f() ’/var/log/apache2/access.log’ <img src="images/img-0006.png" alt="$\backslash $" style="vertical-align:-5px; 
                                     width:7px; 
                                     height:18px" class="math gen" /></tt><br /><tt class="tt"> using time_julianday($7,$6,$5,$8,$9,$10) binwidth 1/24</tt><br /><tt class="tt">tabulate f(x) with format "%16f %16f"</tt> </p></td>

</tr><tr>

    
    <td style="text-align:left; border-right:1px solid black; border-left:1px solid black"><p>Having stored our histogram in the file <tt class="tt">apache.dat</tt>, we now plot the resulting histogram, labelling the horizontal axis with the days of the week. The commands used to achieve this will be introduced in Chapter <a href="ch-plotting.html">1</a>. Note that the major axis ticks along the horizontal axis are placed not at integer Julian Days, which fall at midday on each day, but at —<img src="images/img-0160.png" alt="$.5$" style="vertical-align:0px; 
                                     width:12px; 
                                     height:13px" class="math gen" />, which falls at midnight on each day. Minor axis ticks are placed along the axis every quarter day, i.e. every six hours. </p></td>

</tr><tr>

    
    <td style="text-align:left; border-right:1px solid black; border-left:1px solid black"><p><tt class="tt">set xlabel ’Day’</tt><br /><tt class="tt">set ylabel ’Rate of downloads per day’</tt><br /><tt class="tt">set xtics 0.5, 1</tt><br /><tt class="tt">set mxtics 0.5, 0.25</tt><br /><tt class="tt">set xformat "%s"%(time_dayweekname(x,0)) rotate unit(30*deg)</tt><br /><tt class="tt">plot "apache.dat" notitle with lines</tt> </p></td>

</tr><tr>

    
    <td style="text-align:left; border-right:1px solid black; border-left:1px solid black"><p>The plot below shows the graph which results on a moderately busy webserver which hosts, among many other sites, the PyXPlot website: </p></td>

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    <td style="border-bottom-style:solid; border-bottom-width:1px; border-left:1px solid black; border-right:1px solid black; text-align:left; border-bottom-color:black"><p><center>
<img src="images/img-0162.png" alt="\includegraphics[width=\textwidth ]{examples/eps/ex_apachelog}" style="width:" /></center>  </p></td>

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