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61<h1>Determinant<br>
62<small>
63[<a class="el" href="group__algebra.html">Linear Algebra</a>]</small>
64</h1><table border="0" cellpadding="0" cellspacing="0">
65<tr><td></td></tr>
66<tr><td colspan="2"><br><h2>Functions</h2></td></tr>
67<tr><td class="memItemLeft" nowrap align="right" valign="top">double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__determinant.html#g922f8248470a73dfb9f002a59de9b335">itpp::det</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &amp;X)</td></tr>
68
69<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Determinant of real square matrix.<p>
70Calculate determinant of the real matrix <img class="formulaInl" alt="$\mathbf{X}$" src="form_125.png">.  <a href="#g922f8248470a73dfb9f002a59de9b335"></a><br></td></tr>
71<tr><td class="memItemLeft" nowrap align="right" valign="top">std::complex&lt; double &gt;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__determinant.html#gd9ded34e98aba6036329f53e8abf51a8">itpp::det</a> (const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &amp;X)</td></tr>
72
73<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Determinant of complex square matrix.<p>
74Calculate determinant of the complex matrix <img class="formulaInl" alt="$\mathbf{X}$" src="form_125.png">.  <a href="#gd9ded34e98aba6036329f53e8abf51a8"></a><br></td></tr>
75</table>
76<hr><h2>Function Documentation</h2>
77<a class="anchor" name="gd9ded34e98aba6036329f53e8abf51a8"></a><!-- doxytag: member="itpp::det" ref="gd9ded34e98aba6036329f53e8abf51a8" args="(const cmat &amp;X)" -->
78<div class="memitem">
79<div class="memproto">
80      <table class="memname">
81        <tr>
82          <td class="memname">std::complex&lt; double &gt; itpp::det           </td>
83          <td>(</td>
84          <td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &amp;&nbsp;</td>
85          <td class="paramname"> <em>X</em>          </td>
86          <td>&nbsp;)&nbsp;</td>
87          <td></td>
88        </tr>
89      </table>
90</div>
91<div class="memdoc">
92
93<p>
94Determinant of complex square matrix.<p>
95Calculate determinant of the complex matrix <img class="formulaInl" alt="$\mathbf{X}$" src="form_125.png">.
96<p>
97Uses LU-factorisation. <p class="formulaDsp">
98<img class="formulaDsp" alt="\[ \det(\mathbf{X}) = \det(\mathbf{P}^T \mathbf{L}) \det(\mathbf{U}) = \det(\mathbf{P}^T) \prod(\mathrm{diag}(\mathbf{U})) \]" src="form_130.png">
99<p>
100 and the determinant of the permuation matrix is <img class="formulaInl" alt="$ \pm 1$" src="form_131.png"> depending on the number of row permutations
101<p>References <a class="el" href="itassert_8h-source.html#l00107">it_assert_debug</a>, and <a class="el" href="lu_8cpp-source.html#l00123">itpp::lu()</a>.</p>
102
103<p>Referenced by <a class="el" href="libKF_8cpp-source.html#l00087">bdm::EKFfull::bayes()</a>, <a class="el" href="libKF_8cpp-source.html#l00033">bdm::KalmanFull::bayes()</a>, <a class="el" href="ekf__obj_8cpp-source.html#l00010">EKFfixed::bayes()</a>, <a class="el" href="libDC_8h-source.html#l00156">fsqmat::logdet()</a>, and <a class="el" href="mog__generic_8cpp-source.html#l00279">itpp::MOG_generic::setup_covs()</a>.</p>
104
105</div>
106</div><p>
107<a class="anchor" name="g922f8248470a73dfb9f002a59de9b335"></a><!-- doxytag: member="itpp::det" ref="g922f8248470a73dfb9f002a59de9b335" args="(const mat &amp;X)" -->
108<div class="memitem">
109<div class="memproto">
110      <table class="memname">
111        <tr>
112          <td class="memname">double itpp::det           </td>
113          <td>(</td>
114          <td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &amp;&nbsp;</td>
115          <td class="paramname"> <em>X</em>          </td>
116          <td>&nbsp;)&nbsp;</td>
117          <td></td>
118        </tr>
119      </table>
120</div>
121<div class="memdoc">
122
123<p>
124Determinant of real square matrix.<p>
125Calculate determinant of the real matrix <img class="formulaInl" alt="$\mathbf{X}$" src="form_125.png">.
126<p>
127Uses LU-factorisation. <p class="formulaDsp">
128<img class="formulaDsp" alt="\[ \det(\mathbf{X}) = \det(\mathbf{P}^T \mathbf{L}) \det(\mathbf{U}) = \det(\mathbf{P}^T) \prod(\mathrm{diag}(\mathbf{U})) \]" src="form_130.png">
129<p>
130 and the determinant of the permuation matrix is <img class="formulaInl" alt="$ \pm 1$" src="form_131.png"> depending on the number of row permutations
131<p>References <a class="el" href="itassert_8h-source.html#l00107">it_assert_debug</a>, and <a class="el" href="lu_8cpp-source.html#l00123">itpp::lu()</a>.</p>
132
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