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<div class="title">COND Condition Number of a Matrix </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 condition number of a matrix. To compute the 2-norm condition number of a matrix (ratio of largest to smallest singular values), use the syntax </p>
<pre class="fragment"> y = cond(A)
</pre><p> where A is a matrix. If you want to compute the condition number in a different norm (e.g., the 1-norm), use the second syntax </p>
<pre class="fragment"> y = cond(A,p)
</pre><p> where <code>p</code> is the norm to use when computing the condition number. 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>
<h1><a class="anchor" id="Function"></a>
Internals</h1>
<p>The condition number is defined as </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \frac{\|A\|_p}{\|A^{-1}\|_p} \]" src="form_0.png"/>
</p>
<p> This equation is precisely how the condition number is computed for the case <code>p ~= 2</code>. For the <code>p=2</code> case, the condition number can be computed much more efficiently using the ratio of the largest and smallest singular values. </p>
<h1><a class="anchor" id="Example"></a>
Example</h1>
<p>The condition number of this matrix is large</p>
<pre class="fragment">--> A = [1,1;0,1e-15]
A =
1.0000 1.0000
0 0.0000
--> cond(A)
ans =
2.0000e+15
--> cond(A,1)
ans =
2000000000000002
</pre><p>You can also (for the case <code>p=1</code> use <code>rcond</code> to calculate an estimate of the condition number</p>
<pre class="fragment">--> 1/rcond(A)
ans =
2.0000e+15
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