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<div class="title">PLUS Addition Operator </div> </div>
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<div class="textblock"><p>Section: <a class="el" href="sec_operators.html">Mathematical Operators</a> </p>
<h1><a class="anchor" id="Usage"></a>
Usage</h1>
<p>Adds two numerical arrays (elementwise) together. There are two forms for its use, both with the same general syntax: </p>
<pre class="fragment"> y = a + b
</pre><p> where <code>a</code> and <code>b</code> are <code>n</code>-dimensional arrays of numerical type. In the first case, the two arguments are the same size, in which case, the output <code>y</code> is the same size as the inputs, and is the element-wise the sum of <code>a</code> and <code>b</code>. In the second case, either <code>a</code> or <code>b</code> is a scalar, in which case <code>y</code> is the same size as the larger argument, and is the sum of the scalar added to each element of the other argument.</p>
<p>The rules for manipulating types has changed in FreeMat 4.0. See <code>typerules</code> for more details.</p>
<h1><a class="anchor" id="Function"></a>
Internals</h1>
<p>There are three formulae for the addition operator, depending on the sizes of the three arguments. In the most general case, in which the two arguments are the same size, the output is computed via: </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ y(m_1,\ldots,m_d) = a(m_1,\ldots,m_d) + b(m_1,\ldots,m_d) \]" src="form_129.png"/>
</p>
<p> If <code>a</code> is a scalar, then the output is computed via </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ y(m_1,\ldots,m_d) = a + b(m_1,\ldots,m_d). \]" src="form_130.png"/>
</p>
<p> On the other hand, if <code>b</code> is a scalar, then the output is computed via </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ y(m_1,\ldots,m_d) = a(m_1,\ldots,m_d) + b. \]" src="form_131.png"/>
</p>
<h1><a class="anchor" id="Examples"></a>
Examples</h1>
<p>Here are some examples of using the addition operator. First, a straight-forward usage of the plus operator. The first example is straightforward:</p>
<pre class="fragment">--> 3 + 8
ans =
11
</pre><p>Next, we add a scalar to a vector of values:</p>
<pre class="fragment">--> 3.1 + [2,4,5,6,7]
ans =
5.1000 7.1000 8.1000 9.1000 10.1000
</pre><p>With complex values</p>
<pre class="fragment">--> a = 3 + 4*i
a =
3.0000 + 4.0000i
--> b = a + 2
b =
5.0000 + 4.0000i
</pre><p>Finally, the element-wise version:</p>
<pre class="fragment">--> a = [1,2;3,4]
a =
1 2
3 4
--> b = [2,3;6,7]
b =
2 3
6 7
--> c = a + b
c =
3 5
9 11
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