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<div class="title">NORM Norm Calculation </div> </div>
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<div class="textblock"><p>Section: <a class="el" href="sec_array.html">Array Generation and Manipulations</a> </p>
<h1><a class="anchor" id="Usage"></a>
Usage</h1>
<p>Calculates the norm of a matrix. There are two ways to use the <code>norm</code> function. The general syntax is </p>
<pre class="fragment"> y = norm(A,p)
</pre><p> where <code>A</code> is the matrix to analyze, and <code>p</code> is the type norm to compute. The following choices of <code>p</code> are supported </p>
<ul>
<li>
<code>p = 1</code> returns the 1-norm, or the max column sum of A </li>
<li>
<code>p = 2</code> returns the 2-norm (largest singular value of A) </li>
<li>
<code>p = inf</code> returns the infinity norm, or the max row sum of A </li>
<li>
<code>p = 'fro'</code> returns the Frobenius-norm (vector Euclidean norm, or RMS value) </li>
</ul>
<p>For a vector, the regular norm calculations are performed: </p>
<ul>
<li>
<code>1 <= p < inf</code> returns <code>sum(abs(A).^p)^(1/p)</code> </li>
<li>
<code>p</code> unspecified returns <code>norm(A,2)</code> </li>
<li>
<code>p = inf</code> returns max(abs(A)) </li>
<li>
<code>p = -inf</code> returns min(abs(A)) </li>
</ul>
<h1><a class="anchor" id="Examples"></a>
Examples</h1>
<p>Here are the various norms calculated for a sample matrix</p>
<pre class="fragment">--> A = float(rand(3,4))
A =
0.8462 0.9465 0.6874 0.8668
0.1218 0.9206 0.5877 0.5837
0.7081 0.6608 0.2035 0.5083
--> norm(A,1)
ans =
2.5280
--> norm(A,2)
ans =
2.2997
--> norm(A,inf)
ans =
3.3470
--> norm(A,'fro')
ans =
2.3712
</pre><p>Next, we calculate some vector norms.</p>
<pre class="fragment">--> A = float(rand(4,1))
A =
0.3458
0.1427
0.3998
0.7194
--> norm(A,1)
ans =
1.6078
--> norm(A,2)
ans =
0.9041
--> norm(A,7)
ans =
0.7217
--> norm(A,inf)
ans =
0.7194
--> norm(A,-inf)
ans =
0.1427
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