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log_det.html
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log_det.html
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<h1>Log-Determinant</h1>
<small class="dont-index">Source: <a href='https://github.com/cvxgrp/CVXR/blob/master/R/exports.R'><code>R/exports.R</code></a></small>
<div class="hidden name"><code>log_det.Rd</code></div>
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<div class="ref-description">
<p>The natural logarithm of the determinant of a matrix, \(\log\det(A)\).</p>
</div>
<pre class="usage"><span class='fu'>log_det</span>(<span class='no'>A</span>)</pre>
<h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
<table class="ref-arguments">
<colgroup><col class="name" /><col class="desc" /></colgroup>
<tr>
<th>A</th>
<td><p>An <a href='Expression-class.html'>Expression</a> or matrix.</p></td>
</tr>
</table>
<h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2>
<p>An <a href='Expression-class.html'>Expression</a> representing the log-determinant of the input.</p>
<h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
<pre class="examples"><div class='input'><span class='no'>x</span> <span class='kw'><-</span> <span class='fu'><a href='transpose.html'>t</a></span>(<span class='fu'><a href='https://rdrr.io/r/base/data.frame.html'>data.frame</a></span>(<span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='fl'>0.55</span>, <span class='fl'>0.25</span>, -<span class='fl'>0.2</span>, -<span class='fl'>0.25</span>, -<span class='fl'>0.0</span>, <span class='fl'>0.4</span>),
<span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='fl'>0.0</span>, <span class='fl'>0.35</span>, <span class='fl'>0.2</span>, -<span class='fl'>0.1</span>, -<span class='fl'>0.3</span>, -<span class='fl'>0.2</span>)))
<span class='no'>n</span> <span class='kw'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/nrow.html'>nrow</a></span>(<span class='no'>x</span>)
<span class='no'>m</span> <span class='kw'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/nrow.html'>ncol</a></span>(<span class='no'>x</span>)
<span class='no'>A</span> <span class='kw'><-</span> <span class='fu'><a href='Variable-class.html'>Variable</a></span>(<span class='no'>n</span>,<span class='no'>n</span>)
<span class='no'>b</span> <span class='kw'><-</span> <span class='fu'><a href='Variable-class.html'>Variable</a></span>(<span class='no'>n</span>)
<span class='no'>obj</span> <span class='kw'><-</span> <span class='fu'><a href='Maximize-class.html'>Maximize</a></span>(<span class='fu'>log_det</span>(<span class='no'>A</span>))
<span class='no'>constr</span> <span class='kw'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/lapply.html'>lapply</a></span>(<span class='fl'>1</span>:<span class='no'>m</span>, <span class='kw'>function</span>(<span class='no'>i</span>) { <span class='fu'><a href='p_norm.html'>p_norm</a></span>(<span class='no'>A</span> <span class='kw'>%*%</span> <span class='fu'><a href='https://rdrr.io/r/base/matrix.html'>as.matrix</a></span>(<span class='no'>x</span>[,<span class='no'>i</span>]) + <span class='no'>b</span>) <span class='kw'><=</span> <span class='fl'>1</span> })
<span class='no'>prob</span> <span class='kw'><-</span> <span class='fu'><a href='Problem-class.html'>Problem</a></span>(<span class='no'>obj</span>, <span class='no'>constr</span>)
<span class='no'>result</span> <span class='kw'><-</span> <span class='fu'><a href='psolve.html'>solve</a></span>(<span class='no'>prob</span>)
<span class='no'>result</span>$<span class='no'>value</span></div><div class='output co'>#> [1] 1.974604</div></pre>
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