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<div id="projectname">Algorithms_in_C
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 <span id="projectnumber">1.0.0</span>
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<div id="projectbrief">Set of algorithms implemented in C.</div>
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<div class="header">
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<a href="#func-members">Functions</a> </div>
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<div class="title">realtime_stats.c File Reference</div> </div>
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<div class="contents">
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<p>Compute statistics for data entered in rreal-time.
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<a href="#details">More...</a></p>
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<div class="textblock"><code>#include <assert.h></code><br />
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<code>#include <math.h></code><br />
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<code>#include <stdio.h></code><br />
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</div><div class="textblock"><div class="dynheader">
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Include dependency graph for realtime_stats.c:</div>
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<div class="dyncontent">
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<div class="center"><iframe scrolling="no" frameborder="0" src="../../d2/de9/realtime__stats_8c__incl.svg" width="254" height="127"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
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</div>
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</div>
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</div><table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
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Functions</h2></td></tr>
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<tr class="memitem:a63ddcdaab24f722f0963fa2fbe0ae628"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="../../dc/d47/realtime__stats_8c.html#a63ddcdaab24f722f0963fa2fbe0ae628">stats_computer1</a> (float x, float *mean, float *variance, float *std)</td></tr>
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<tr class="memdesc:a63ddcdaab24f722f0963fa2fbe0ae628"><td class="mdescLeft"> </td><td class="mdescRight">continuous mean and variance computance using first value as an approximation for the mean. <a href="../../dc/d47/realtime__stats_8c.html#a63ddcdaab24f722f0963fa2fbe0ae628">More...</a><br /></td></tr>
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<tr class="separator:a63ddcdaab24f722f0963fa2fbe0ae628"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a34be233a9200ee2065f6b7b27e2d9a96"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="../../dc/d47/realtime__stats_8c.html#a34be233a9200ee2065f6b7b27e2d9a96">stats_computer2</a> (float x, float *mean, float *variance, float *std)</td></tr>
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<tr class="memdesc:a34be233a9200ee2065f6b7b27e2d9a96"><td class="mdescLeft"> </td><td class="mdescRight">continuous mean and variance computance using Welford's algorithm (very accurate) <a href="../../dc/d47/realtime__stats_8c.html#a34be233a9200ee2065f6b7b27e2d9a96">More...</a><br /></td></tr>
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<tr class="separator:a34be233a9200ee2065f6b7b27e2d9a96"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:aa54c915581fcc495489175a4386d59fd"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="../../dc/d47/realtime__stats_8c.html#aa54c915581fcc495489175a4386d59fd">test_function</a> (const float *test_data, const int number_of_samples)</td></tr>
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<tr class="memdesc:aa54c915581fcc495489175a4386d59fd"><td class="mdescLeft"> </td><td class="mdescRight">Test the algorithm implementation. <a href="../../dc/d47/realtime__stats_8c.html#aa54c915581fcc495489175a4386d59fd">More...</a><br /></td></tr>
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<tr class="separator:aa54c915581fcc495489175a4386d59fd"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a3c04138a5bfe5d72780bb7e82a18e627"><td class="memItemLeft" align="right" valign="top"><a id="a3c04138a5bfe5d72780bb7e82a18e627"></a>
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int </td><td class="memItemRight" valign="bottom"><a class="el" href="../../dc/d47/realtime__stats_8c.html#a3c04138a5bfe5d72780bb7e82a18e627">main</a> (int argc, char **argv)</td></tr>
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<tr class="memdesc:a3c04138a5bfe5d72780bb7e82a18e627"><td class="mdescLeft"> </td><td class="mdescRight">Main function. <br /></td></tr>
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<tr class="separator:a3c04138a5bfe5d72780bb7e82a18e627"><td class="memSeparator" colspan="2"> </td></tr>
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</table>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
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<div class="textblock"><p>Compute statistics for data entered in rreal-time. </p>
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<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala">Krishna Vedala</a></dd></dl>
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<p>This algorithm is really beneficial to compute statistics on data read in realtime. For example, devices reading biometrics data. The algorithm is simple enough to be easily implemented in an embedded system. </p>
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</div><h2 class="groupheader">Function Documentation</h2>
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<a id="a63ddcdaab24f722f0963fa2fbe0ae628"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a63ddcdaab24f722f0963fa2fbe0ae628">◆ </a></span>stats_computer1()</h2>
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<div class="memitem">
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<div class="memproto">
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<table class="memname">
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<tr>
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<td class="memname">void stats_computer1 </td>
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<td>(</td>
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<td class="paramtype">float </td>
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<td class="paramname"><em>x</em>, </td>
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</tr>
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<tr>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">float * </td>
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<td class="paramname"><em>mean</em>, </td>
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</tr>
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<tr>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">float * </td>
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<td class="paramname"><em>variance</em>, </td>
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</tr>
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<tr>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">float * </td>
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<td class="paramname"><em>std</em> </td>
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</tr>
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<tr>
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<td></td>
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<td>)</td>
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<td></td><td></td>
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</tr>
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</table>
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</div><div class="memdoc">
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<p>continuous mean and variance computance using first value as an approximation for the mean. </p>
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<p>If the first number is much far form the mean, the algorithm becomes very inaccurate to compute variance and standard deviation. </p><dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramdir">[in]</td><td class="paramname">x</td><td>new value added to data set </td></tr>
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<tr><td class="paramdir">[out]</td><td class="paramname">mean</td><td>if not NULL, mean returns mean of data set </td></tr>
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<tr><td class="paramdir">[out]</td><td class="paramname">variance</td><td>if not NULL, mean returns variance of data set </td></tr>
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<tr><td class="paramdir">[out]</td><td class="paramname">std</td><td>if not NULL, mean returns standard deviation of data set </td></tr>
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</table>
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</dd>
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</dl>
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<div class="fragment"><div class="line"><a name="l00025"></a><span class="lineno"> 25</span> {</div>
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<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  <span class="comment">/* following variables declared static becuase they need to be remembered</span></div>
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<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="comment"> * when updating for next sample, when received.</span></div>
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<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="comment"> */</span></div>
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<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>  <span class="keyword">static</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> n = 0;</div>
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<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>  <span class="keyword">static</span> <span class="keywordtype">float</span> Ex = 0.f, Ex2 = 0.f;</div>
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<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  <span class="keyword">static</span> <span class="keywordtype">float</span> K = 0.f;</div>
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<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  </div>
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<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  <span class="keywordflow">if</span> (n == 0)</div>
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<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  K = x;</div>
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<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  n++;</div>
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<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  <span class="keywordtype">float</span> tmp = x - K;</div>
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<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  Ex += tmp;</div>
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<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  Ex2 += tmp * tmp;</div>
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<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  </div>
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<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  <span class="comment">/* return sample mean computed till last sample */</span></div>
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<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  <span class="keywordflow">if</span> (mean != NULL)</div>
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<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  *mean = K + Ex / n;</div>
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<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  </div>
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<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  <span class="comment">/* return data variance computed till last sample */</span></div>
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<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  <span class="keywordflow">if</span> (variance != NULL)</div>
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<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  *variance = (Ex2 - (Ex * Ex) / n) / (n - 1);</div>
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<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  </div>
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<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  <span class="comment">/* return sample standard deviation computed till last sample */</span></div>
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<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  <span class="keywordflow">if</span> (std != NULL)</div>
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<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  *std = sqrtf(*variance);</div>
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<div class="line"><a name="l00051"></a><span class="lineno"> 51</span> }</div>
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</div><!-- fragment -->
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</div>
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</div>
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<a id="a34be233a9200ee2065f6b7b27e2d9a96"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a34be233a9200ee2065f6b7b27e2d9a96">◆ </a></span>stats_computer2()</h2>
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<div class="memitem">
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<div class="memproto">
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<table class="memname">
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<tr>
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<td class="memname">void stats_computer2 </td>
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<td>(</td>
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<td class="paramtype">float </td>
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<td class="paramname"><em>x</em>, </td>
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</tr>
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<tr>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">float * </td>
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<td class="paramname"><em>mean</em>, </td>
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</tr>
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<tr>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">float * </td>
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<td class="paramname"><em>variance</em>, </td>
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</tr>
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<tr>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">float * </td>
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<td class="paramname"><em>std</em> </td>
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</tr>
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<tr>
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<td></td>
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<td>)</td>
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<td></td><td></td>
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</tr>
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</table>
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</div><div class="memdoc">
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<p>continuous mean and variance computance using Welford's algorithm (very accurate) </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramdir">[in]</td><td class="paramname">x</td><td>new value added to data set </td></tr>
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<tr><td class="paramdir">[out]</td><td class="paramname">mean</td><td>if not NULL, mean returns mean of data set </td></tr>
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<tr><td class="paramdir">[out]</td><td class="paramname">variance</td><td>if not NULL, mean returns variance of data set </td></tr>
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<tr><td class="paramdir">[out]</td><td class="paramname">std</td><td>if not NULL, mean returns standard deviation of data set </td></tr>
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</table>
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</dd>
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</dl>
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<div class="fragment"><div class="line"><a name="l00062"></a><span class="lineno"> 62</span> {</div>
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<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <span class="comment">/* following variables declared static becuase they need to be remembered</span></div>
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<div class="line"><a name="l00064"></a><span class="lineno"> 64</span> <span class="comment"> * when updating for next sample, when received.</span></div>
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<div class="line"><a name="l00065"></a><span class="lineno"> 65</span> <span class="comment"> */</span></div>
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<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <span class="keyword">static</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> n = 0;</div>
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<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <span class="keyword">static</span> <span class="keywordtype">float</span> mu = 0, M = 0;</div>
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<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  </div>
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<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  n++;</div>
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<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="keywordtype">float</span> delta = x - mu;</div>
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<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  mu += delta / n;</div>
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<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  <span class="keywordtype">float</span> delta2 = x - mu;</div>
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<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  M += delta * delta2;</div>
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<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  </div>
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<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="comment">/* return sample mean computed till last sample */</span></div>
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<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <span class="keywordflow">if</span> (mean != NULL)</div>
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<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  *mean = mu;</div>
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<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  </div>
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<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <span class="comment">/* return data variance computed till last sample */</span></div>
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<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  <span class="keywordflow">if</span> (variance != NULL)</div>
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<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  *variance = M / n;</div>
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<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  </div>
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<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <span class="comment">/* return sample standard deviation computed till last sample */</span></div>
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<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <span class="keywordflow">if</span> (std != NULL)</div>
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<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  *std = sqrtf(*variance);</div>
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<div class="line"><a name="l00086"></a><span class="lineno"> 86</span> }</div>
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</div><!-- fragment -->
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<a id="aa54c915581fcc495489175a4386d59fd"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#aa54c915581fcc495489175a4386d59fd">◆ </a></span>test_function()</h2>
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<div class="memitem">
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<div class="memproto">
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<table class="memname">
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<tr>
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<td class="memname">void test_function </td>
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<td>(</td>
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<td class="paramtype">const float * </td>
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<td class="paramname"><em>test_data</em>, </td>
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</tr>
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<tr>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">const int </td>
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<td class="paramname"><em>number_of_samples</em> </td>
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</tr>
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<tr>
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<td></td>
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<td>)</td>
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<td></td><td></td>
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</div><div class="memdoc">
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<p>Test the algorithm implementation. </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramdir">[in]</td><td class="paramname">test_data</td><td>array of data to test the algorithms </td></tr>
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<tr><td class="paramdir">[in]</td><td class="paramname">number_of_samples</td><td>number of samples of data </td></tr>
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</table>
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</dd>
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</dl>
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<div class="fragment"><div class="line"><a name="l00093"></a><span class="lineno"> 93</span> {</div>
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<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  <span class="keywordtype">float</span> ref_mean = 0.f, ref_variance = 0.f;</div>
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<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  <span class="keywordtype">float</span> s1_mean = 0.f, s1_variance = 0.f, s1_std = 0.f;</div>
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<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  <span class="keywordtype">float</span> s2_mean = 0.f, s2_variance = 0.f, s2_std = 0.f;</div>
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<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  </div>
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<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < number_of_samples; i++)</div>
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<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  {</div>
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<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  <a class="code" href="../../dc/d47/realtime__stats_8c.html#a63ddcdaab24f722f0963fa2fbe0ae628">stats_computer1</a>(test_data[i], &s1_mean, &s1_variance, &s1_std);</div>
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<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  <a class="code" href="../../dc/d47/realtime__stats_8c.html#a34be233a9200ee2065f6b7b27e2d9a96">stats_computer2</a>(test_data[i], &s2_mean, &s2_variance, &s2_std);</div>
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<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  ref_mean += test_data[i];</div>
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<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  }</div>
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<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  ref_mean /= number_of_samples;</div>
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<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  </div>
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<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < number_of_samples; i++)</div>
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<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  {</div>
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<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  <span class="keywordtype">float</span> temp = test_data[i] - ref_mean;</div>
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<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  ref_variance += temp * temp;</div>
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<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  }</div>
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<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  ref_variance /= number_of_samples;</div>
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<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  </div>
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<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  printf(<span class="stringliteral">"<<<<<<<< Test Function >>>>>>>>\n"</span>);</div>
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<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  printf(<span class="stringliteral">"Expected: Mean: %.4f\t Variance: %.4f\n"</span>, ref_mean, ref_variance);</div>
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<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  printf(<span class="stringliteral">"\tMethod 1:\tMean: %.4f\t Variance: %.4f\t Std: %.4f\n"</span>, s1_mean,</div>
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<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  s1_variance, s1_std);</div>
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<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  printf(<span class="stringliteral">"\tMethod 2:\tMean: %.4f\t Variance: %.4f\t Std: %.4f\n"</span>, s2_mean,</div>
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<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  s2_variance, s2_std);</div>
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<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  </div>
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<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  assert(fabs(s1_mean - ref_mean) < 0.01);</div>
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<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  assert(fabs(s2_mean - ref_mean) < 0.01);</div>
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<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  assert(fabs(s2_variance - ref_variance) < 0.01);</div>
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<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  </div>
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<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  printf(<span class="stringliteral">"(Tests passed)\n\n"</span>);</div>
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<div class="line"><a name="l00125"></a><span class="lineno"> 125</span> }</div>
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<div class="ttc" id="arealtime__stats_8c_html_a34be233a9200ee2065f6b7b27e2d9a96"><div class="ttname"><a href="../../dc/d47/realtime__stats_8c.html#a34be233a9200ee2065f6b7b27e2d9a96">stats_computer2</a></div><div class="ttdeci">void stats_computer2(float x, float *mean, float *variance, float *std)</div><div class="ttdoc">continuous mean and variance computance using Welford's algorithm (very accurate)</div><div class="ttdef"><b>Definition:</b> realtime_stats.c:61</div></div>
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<div class="ttc" id="arealtime__stats_8c_html_a63ddcdaab24f722f0963fa2fbe0ae628"><div class="ttname"><a href="../../dc/d47/realtime__stats_8c.html#a63ddcdaab24f722f0963fa2fbe0ae628">stats_computer1</a></div><div class="ttdeci">void stats_computer1(float x, float *mean, float *variance, float *std)</div><div class="ttdoc">continuous mean and variance computance using first value as an approximation for the mean.</div><div class="ttdef"><b>Definition:</b> realtime_stats.c:24</div></div>
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