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<div class="title">DOTTIMES Element-wise Multiplication 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>Multiplies two numerical arrays (elementwise). 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 product 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 product of the scalar with 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 dot-times 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="\[ y(m_1,\ldots,m_d) = a(m_1,\ldots,m_d) \times b(m_1,\ldots,m_d) \]" src="form_105.png"/>
</p>
<p> If <code>a</code> is a scalar, then the output is computed via </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ y(m_1,\ldots,m_d) = a \times b(m_1,\ldots,m_d). \]" src="form_106.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="\[ y(m_1,\ldots,m_d) = a(m_1,\ldots,m_d) \times b. \]" src="form_107.png"/>
</p>
<h1><a class="anchor" id="Examples"></a>
Examples</h1>
<p>Here are some examples of using the dottimes operator. First, a straight-forward usage of the <code>.*</code> operator. The first example is straightforward:</p>
<pre class="fragment">--> 3 .* 8
ans =
24
</pre><p>Next, we multiply a scalar by a vector of values:</p>
<pre class="fragment">--> 3.1 .* [2,4,5,6,7]
ans =
6.2000 12.4000 15.5000 18.6000 21.7000
</pre><p>With complex values</p>
<pre class="fragment">--> a = 3 + 4*i
a =
3.0000 + 4.0000i
--> b = a .* 2
b =
6.0000 + 8.0000i
</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 =
2 6
18 28
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