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<div class="title">DOTPOWER Element-wise Power 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>Raises one numerical array to another array (elementwise). There are three operators all with the same general syntax: </p>
<pre class="fragment"> y = a .^ b
</pre><p> The result <code>y</code> depends on which of the following three situations applies to the arguments <code>a</code> and <code>b</code>: </p>
<ol>
<li>
<code>a</code> is a scalar, <code>b</code> is an arbitrary <code>n</code>-dimensional numerical array, in which case the output is <code>a</code> raised to the power of each element of <code>b</code>, and the output is the same size as <code>b</code>. </li>
<li>
<code>a</code> is an <code>n</code>-dimensional numerical array, and <code>b</code> is a scalar, then the output is the same size as <code>a</code>, and is defined by each element of <code>a</code> raised to the power <code>b</code>. </li>
<li>
<code>a</code> and <code>b</code> are both <code>n</code>-dimensional numerical arrays of <b>the same size</b>. In this case, each element of the output is the corresponding element of <code>a</code> raised to the power defined by the corresponding element of <code>b</code>. </li>
</ol>
<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 this operator. For the first form </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ y(m_1,\ldots,m_d) = a^{b(m_1,\ldots,m_d)}, \]" src="form_99.png"/>
</p>
<p> and the second form </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ y(m_1,\ldots,m_d) = a(m_1,\ldots,m_d)^b, \]" src="form_100.png"/>
</p>
<p> and in the third form </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_101.png"/>
</p>
<h1><a class="anchor" id="Examples"></a>
Examples</h1>
<p>We demonstrate the three forms of the dot-power operator using some simple examples. First, the case of a scalar raised to a series of values.</p>
<pre class="fragment">--> a = 2
a =
2
--> b = 1:4
b =
1 2 3 4
--> c = a.^b
c =
2 4 8 16
</pre><p>The second case shows a vector raised to a scalar.</p>
<pre class="fragment">--> c = b.^a
c =
1 4 9 16
</pre><p>The third case shows the most general use of the dot-power operator.</p>
<pre class="fragment">--> A = [1,2;3,2]
A =
1 2
3 2
--> B = [2,1.5;0.5,0.6]
B =
2.0000 1.5000
0.5000 0.6000
--> C = A.^B
C =
1.0000 2.8284
1.7321 1.5157
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