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<div class="title">COV Covariance Matrix </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 covariance of a matrix or a vector. The general syntax for its use is </p>
<pre class="fragment"> y = cov(x)
</pre><p> where <code>x</code> is a matrix or a vector. If <code>x</code> is a vector then <code>cov</code> returns the variance of <code>x</code>. If <code>x</code> is a matrix then <code>cov</code> returns the covariance matrix of the columns of <code>x</code>. You can also call <code>cov</code> with two arguments to compute the matrix of cross correlations. The syntax for this mode is </p>
<pre class="fragment"> y = cov(x,z)
</pre><p> where <code>x</code> and <code>z</code> are matrices of the same size. Finally, you can provide a normalization flag <code>d</code> that is either <code>0</code> or <code>1</code>, which changes the normalization factor from <code>L-1</code> (for <code>d=0</code>) to <code>L</code> (for <code>d=1</code>) where <code>L</code> is the number of rows in the matrix <code>x</code>. In this case, the syntaxes are </p>
<pre class="fragment"> y = cov(x,z,d)
</pre><p> for the two-argument case, and </p>
<pre class="fragment"> y = cov(x,d)
</pre><p> for the one-argument case. </p>
<h1><a class="anchor" id="Example"></a>
Example</h1>
<p>The following demonstrates some uses of the <code>cov</code> 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
--> B = [4,-2,0;1,5,2;-2,0,1];
</pre><p>We start with the covariance matrix for <code>A</code></p>
<pre class="fragment">--> cov(A)
ans =
4.2222 -1.6667 1.5556
-1.6667 0.6667 -0.6667
1.5556 -0.6667 0.8889
</pre><p>and again with the (biased) normalization</p>
<pre class="fragment">--> cov(A,1)
ans =
4.2222 -1.6667 1.5556
-1.6667 0.6667 -0.6667
1.5556 -0.6667 0.8889
</pre><p>Here we compute the cross covariance between <code>A</code> and <code>B</code></p>
<pre class="fragment">--> cov(A,B)
ans =
2.0988 1.6667
1.6667 5.1111
</pre><p>and again with biased normalization</p>
<pre class="fragment">--> cov(A,B,1)
ans =
2.0988 1.6667
1.6667 5.1111
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