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<div class="title">SUM Sum Function </div> </div>
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<div class="textblock"><p>Section: <a class="el" href="sec_elementary.html">Elementary Functions</a> </p>
<h1><a class="anchor" id="Usage"></a>
Usage</h1>
<p>Computes the summation of an array along a given dimension. The general syntax for its use is </p>
<pre class="fragment"> y = sum(x,d)
</pre><p> where <code>x</code> is an <code>n</code>-dimensions array of numerical type. The output is of the same numerical type as the input. The argument <code>d</code> is optional, and denotes the dimension along which to take the summation. The output <code>y</code> is the same size as <code>x</code>, except that it is singular along the summation direction. So, for example, if <code>x</code> is a <code>3 x 3 x 4</code> array, and we compute the summation along dimension <code>d=2</code>, then the output is of size <code>3 x 1 x 4</code>. </p>
<h1><a class="anchor" id="Function"></a>
Internals</h1>
<p>The output is computed via </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ y(m_1,\ldots,m_{d-1},1,m_{d+1},\ldots,m_{p}) = \sum_{k} x(m_1,\ldots,m_{d-1},k,m_{d+1},\ldots,m_{p}) \]" src="form_27.png"/>
</p>
<p> If <code>d</code> is omitted, then the summation is taken along the first non-singleton dimension of <code>x</code>. </p>
<h1><a class="anchor" id="Example"></a>
Example</h1>
<p>The following piece of code demonstrates various uses of the summation function</p>
<pre class="fragment">--> A = [5,1,3;3,2,1;0,3,1]
A =
5 1 3
3 2 1
0 3 1
</pre><p>We start by calling <code>sum</code> without a dimension argument, in which case it defaults to the first nonsingular dimension (in this case, along the columns or <code>d = 1</code>).</p>
<pre class="fragment">--> sum(A)
ans =
8 6 5
</pre><p>Next, we take the sum along the rows.</p>
<pre class="fragment">--> sum(A,2)
ans =
9
6
4
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